混沌理论 (Chinese Wikipedia)

Gardini, Laura; Grebogi, Celso; Lenci, Stefano. Chaos theory and applications: a retrospective on lessons learned and missed or new opportunities. Nonlinear Dynamics. 2020-10-01, 102 (2): 643–644. ISSN 1573-269X. doi:10.1007/s11071-020-05903-0 （英语）.
Poincaré, Jules Henri. Sur le problème des trois corps et les équations de la dynamique. Divergence des séries de M. Lindstedt. Acta Mathematica. 1890, 13 (1–2): 1–270. doi:10.1007/BF02392506 .
Kolmogorov, Andrey Nikolaevich. Local structure of turbulence in an incompressible fluid for very large Reynolds numbers. Doklady Akademii Nauk SSSR. 1941, 30 (4): 301–5. Bibcode:1941DoSSR..30..301K. Reprinted in: Kolmogorov, A. N. The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers. Proceedings of the Royal Society A. 1991, 434 (1890): 9–13. Bibcode:1991RSPSA.434....9K. S2CID 123612939. doi:10.1098/rspa.1991.0075.
Kolmogorov, A. N. On degeneration of isotropic turbulence in an incompressible viscous liquid. Doklady Akademii Nauk SSSR. 1941, 31 (6): 538–540. Reprinted in: Kolmogorov, A. N. Dissipation of Energy in the Locally Isotropic Turbulence. Proceedings of the Royal Society A. 1991, 434 (1890): 15–17. Bibcode:1991RSPSA.434...15K. S2CID 122060992. doi:10.1098/rspa.1991.0076.
Kolmogorov, A. N. Preservation of conditionally periodic movements with small change in the Hamilton function. Stochastic Behavior in Classical and Quantum Hamiltonian Systems. Lecture Notes in Physics 98. 1979: 527–530. Bibcode:1979LNP....93...51K. ISBN 978-3-540-09120-2. doi:10.1007/BFb0021737. |journal=被忽略 (帮助) See also Kolmogorov–Arnold–Moser theorem
Cartwright, Mary L.; Littlewood, John E. On non-linear differential equations of the second order, I: The equation y" + k(1−y²)y' + y = bλkcos(λt + a), k large. Journal of the London Mathematical Society. 1945, 20 (3): 180–9. doi:10.1112/jlms/s1-20.3.180. See also: Van der Pol oscillator
Smale, Stephen. Morse inequalities for a dynamical system. Bulletin of the American Mathematical Society. January 1960, 66: 43–49. doi:10.1090/S0002-9904-1960-10386-2 .
Chirikov, B. V. Resonance processes in magnetic traps. The Soviet Journal of Atomic Energy. 1960-12-01, 6 (6): 464–470. ISSN 1573-8205. S2CID 59483478. doi:10.1007/BF01483352 （英语）.
Bellissard, J.; Bohigas, O.; Casati, G.; Shepelyansky, D.L. A pioneer of chaos. Physica D: Nonlinear Phenomena. 1 July 1999, 131 (1–4): viii–xv. Bibcode:1999PhyD..131D...8B. ISSN 0167-2789. S2CID 119107150. doi:10.1016/s0167-2789(99)90007-6.
Lorenz, Edward N. Deterministic non-periodic flow. Journal of the Atmospheric Sciences. 1963, 20 (2): 130–141. Bibcode:1963JAtS...20..130L. doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 .
Berger J.M.; Mandelbrot B. A new model for error clustering in telephone circuits. IBM Journal of Research and Development. 1963, 7 (3): 224–236. doi:10.1147/rd.73.0224.
Mandelbrot, Benoît. How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension. Science. 5 May 1967, 156 (3775): 636–8 [2023-11-15]. Bibcode:1967Sci...156..636M. PMID 17837158. S2CID 15662830. doi:10.1126/science.156.3775.636. （原始内容存档于2021-10-19）.
Feigenbaum, Mitchell. Quantitative universality for a class of nonlinear transformations. Journal of Statistical Physics. July 1978, 19 (1): 25–52. Bibcode:1978JSP....19...25F. CiteSeerX 10.1.1.418.9339 . S2CID 124498882. doi:10.1007/BF01020332.
Huberman, B.A. A Model for Dysfunctions in Smooth Pursuit Eye Movement. Annals of the New York Academy of Sciences. July 1987,. 504 Perspectives in Biological Dynamics and Theoretical Medicine (1): 260–273. Bibcode:1987NYASA.504..260H. PMID 3477120. S2CID 42733652. doi:10.1111/j.1749-6632.1987.tb48737.x.
Bak, Per; Tang, Chao; Wiesenfeld, Kurt. Self-organized criticality: An explanation of the 1/f noise. Physical Review Letters. 1987-07-27, 59 (4): 381–4. Bibcode:1987PhRvL..59..381B. PMID 10035754. S2CID 7674321. doi:10.1103/PhysRevLett.59.381. However, the conclusions of this article have been subject to dispute. ?. （原始内容存档于2007-12-14）. . See especially: Laurson, Lasse; Alava, Mikko J.; Zapperi, Stefano. Letter: Power spectra of self-organized critical sand piles. Journal of Statistical Mechanics: Theory and Experiment. 2005-09-15, 0511. L001.
Motter, A. E.; Campbell, D. K. Chaos at fifty. Phys. Today. 2013, 66 (5): 27–33. Bibcode:2013PhT....66e..27M. S2CID 54005470. arXiv:1306.5777 . doi:10.1063/pt.3.1977.
Hubler, A.; Foster, G.; Phelps, K. Managing chaos: Thinking out of the box. Complexity. 2007, 12 (3): 10. Bibcode:2007Cmplx..12c..10H. doi:10.1002/cplx.20159.
Kiel, L.; Elliott, Euel (编). Chaos Theory in the Social Sciences: Foundations and Applications. Ann Arbor, MI: University of Michigan Press. 1996. ISBN 9780472106387. doi:10.3998/mpub.14623. hdl:2027/fulcrum.d504rm03n （英语）.
Shen, Bo-Wen; Pielke, Sr., Roger; Zeng, Xubin. The 50th Anniversary of the Metaphorical Butterfly Effect since Lorenz (1972): Multistability, Multiscale Predictability, and Sensitivity in Numerical Models.. Atmosphere. 2023-08-12, 14 (8): 1279. Bibcode:2023Atmos..14.1279S. doi:10.3390/atmos14081279 .
Shen, Bo-Wen. A Review of Lorenz's Models from 1960 to 2008. International Journal of Bifurcation and Chaos. 2023-09-04, 33 (10): 2330024. doi:10.1142/S0218127423300240.
Lorenz, E. N. The problem of deducing the climate from the governing equations.. Tellus. 1964, 16 (1): 1–11. Bibcode:1964Tell...16....1L. doi:10.3402/tellusa.v16i1.8893.
Banks; Brooks; Cairns; Davis; Stacey. On Devaney's definition of chaos. The American Mathematical Monthly. 1992, 99 (4): 332–334. doi:10.1080/00029890.1992.11995856.
Vellekoop, Michel; Berglund, Raoul. On Intervals, Transitivity = Chaos. The American Mathematical Monthly. April 1994, 101 (4): 353–5. JSTOR 2975629. doi:10.2307/2975629.
Shen, Bo-Wen; Pielke, Roger A.; Zeng, Xubin. One Saddle Point and Two Types of Sensitivities within the Lorenz 1963 and 1969 Models. Atmosphere. 2022-05-07, 13 (5): 753. Bibcode:2022Atmos..13..753S. ISSN 2073-4433. doi:10.3390/atmos13050753  （英语）.
Werndl, Charlotte. What are the New Implications of Chaos for Unpredictability?. The British Journal for the Philosophy of Science. 2009, 60 (1): 195–220. S2CID 354849. arXiv:1310.1576 . doi:10.1093/bjps/axn053.
Li, T.Y.; Yorke, J.A. Period Three Implies Chaos (PDF). American Mathematical Monthly. 1975, 82 (10): 985–92. Bibcode:1975AmMM...82..985L. CiteSeerX 10.1.1.329.5038 . JSTOR 2318254. doi:10.2307/2318254. （原始内容 (PDF)存档于2009-12-29）.
Strelioff, Christopher; et., al. Medium-Term Prediction of Chaos. Phys. Rev. Lett. 2006, 96 (4): 044101. Bibcode:2006PhRvL..96d4101S. PMID 16486826. doi:10.1103/PhysRevLett.96.044101.
Shen, Bo-Wen. Aggregated Negative Feedback in a Generalized Lorenz Model. International Journal of Bifurcation and Chaos. 2019-03-01, 29 (3): 1950037–1950091. Bibcode:2019IJBC...2950037S. ISSN 0218-1274. S2CID 132494234. doi:10.1142/S0218127419500378 .
Shen, Bo-Wen; Pielke, Roger A.; Zeng, Xubin; Baik, Jong-Jin; Faghih-Naini, Sara; Cui, Jialin; Atlas, Robert. Is Weather Chaotic?: Coexistence of Chaos and Order within a Generalized Lorenz Model. Bulletin of the American Meteorological Society. 2021-01-01, 102 (1): E148–E158. Bibcode:2021BAMS..102E.148S. ISSN 0003-0007. S2CID 208369617. doi:10.1175/BAMS-D-19-0165.1  （英语）.
Shen, Bo-Wen; Pielke Sr., Roger Pielke; Zeng, Xubin; Cui, Jialin; Faghih-Naini, Sara; Paxson, Wei; Kesarkar, Amit; Zeng, Xiping; Atlas, Robert. The Dual Nature of Chaos and Order in the Atmosphere. Atmosphere. 2022-11-12, 13 (11): 1892. Bibcode:2022Atmos..13.1892S. ISSN 2073-4433. doi:10.3390/atmos13111892  （英语）.
Yorke, James A.; Yorke, Ellen D. Metastable chaos: The transition to sustained chaotic behavior in the Lorenz model. Journal of Statistical Physics. 1979-09-01, 21 (3): 263–277. Bibcode:1979JSP....21..263Y. ISSN 1572-9613. S2CID 12172750. doi:10.1007/BF01011469 （英语）.
Shen, Bo-Wen; Pielke Sr., R. A.; Zeng, X.; Baik, J.-J.; Faghih-Naini, S.; Cui, J.; Atlas, R.; Reyes, T. A. L. Is Weather Chaotic? Coexisting Chaotic and Non-chaotic Attractors within Lorenz Models. Skiadas, Christos H.; Dimotikalis, Yiannis (编). 13th Chaotic Modeling and Simulation International Conference. Springer Proceedings in Complexity. Cham: Springer International Publishing. 2021: 805–825 [2023-11-14]. ISBN 978-3-030-70795-8. S2CID 245197840. doi:10.1007/978-3-030-70795-8_57. （原始内容存档于2023-05-28）（英语）.
Okulov, A Yu; Oraevskiĭ, A N. Space–temporal behavior of a light pulse propagating in a nonlinear nondispersive medium. J. Opt. Soc. Am. B. 1986, 3 (5): 741–746. Bibcode:1986JOSAB...3..741O. S2CID 124347430. doi:10.1364/JOSAB.3.000741.
Okulov, A Yu; Oraevskiĭ, A N. Regular and stochastic self-modulation in a ring laser with nonlinear element. Soviet Journal of Quantum Electronics. 1984, 14 (2): 1235–1237. Bibcode:1984QuEle..14.1235O. doi:10.1070/QE1984v014n09ABEH006171.
Sprott, J.C. Simplest dissipative chaotic flow. Physics Letters A. 1997, 228 (4–5): 271–274. Bibcode:1997PhLA..228..271S. doi:10.1016/S0375-9601(97)00088-1.
Fu, Z.; Heidel, J. Non-chaotic behaviour in three-dimensional quadratic systems. Nonlinearity. 1997, 10 (5): 1289–1303. Bibcode:1997Nonli..10.1289F. S2CID 250757113. doi:10.1088/0951-7715/10/5/014.
Heidel, J.; Fu, Z. Nonchaotic behaviour in three-dimensional quadratic systems II. The conservative case. Nonlinearity. 1999, 12 (3): 617–633. Bibcode:1999Nonli..12..617H. S2CID 250853499. doi:10.1088/0951-7715/12/3/012.
Bonet, J.; Martínez-Giménez, F.; Peris, A. A Banach space which admits no chaotic operator. Bulletin of the London Mathematical Society. 2001, 33 (2): 196–8. S2CID 121429354. doi:10.1112/blms/33.2.196.
Shen, Bo-Wen. Nonlinear Feedback in a Five-Dimensional Lorenz Model. Journal of the Atmospheric Sciences. 2014-05-01, 71 (5): 1701–1723. Bibcode:2014JAtS...71.1701S. ISSN 0022-4928. S2CID 123683839. doi:10.1175/JAS-D-13-0223.1 （英语）.
Musielak, Dora E.; Musielak, Zdzislaw E.; Kennamer, Kenny S. The onset of chaos in nonlinear dynamical systems determined with a new fractal technique. Fractals. 2005-03-01, 13 (1): 19–31 [2023-11-14]. ISSN 0218-348X. doi:10.1142/S0218348X0500274X. （原始内容存档于2023-06-03）.
Roy, D.; Musielak, Z. E. Generalized Lorenz models and their routes to chaos. I. Energy-conserving vertical mode truncations. Chaos, Solitons & Fractals. 2007-05-01, 32 (3): 1038–1052. Bibcode:2007CSF....32.1038R. ISSN 0960-0779. doi:10.1016/j.chaos.2006.02.013 （英语）.
Adachihara, H; McLaughlin, D W; Moloney, J V; Newell, A C. Solitary waves as fixed points of infinite-dimensional maps for an optical bistable ring cavity: Analysis. Journal of Mathematical Physics. 1988, 29 (1): 63. Bibcode:1988JMP....29...63A. doi:10.1063/1.528136.
Okulov, A Yu. Spatial soliton laser: geometry and stability. Optics and Spectroscopy. 2000, 89 (1): 145–147. Bibcode:2000OptSp..89..131O. S2CID 122790937. doi:10.1134/BF03356001.
Okulov, A Yu. Structured light entities, chaos and nonlocal maps. Chaos, Solitons & Fractals. 2020, 133 (4): 109638. Bibcode:2020CSF...13309638O. S2CID 118828500. arXiv:1901.09274 . doi:10.1016/j.chaos.2020.109638.
Kyrtsou C.; Labys W. Evidence for chaotic dependence between US inflation and commodity prices. Journal of Macroeconomics. 2006, 28 (1): 256–266. doi:10.1016/j.jmacro.2005.10.019.
Kyrtsou C., Labys W.; Labys. Detecting positive feedback in multivariate time series: the case of metal prices and US inflation. Physica A. 2007, 377 (1): 227–229. Bibcode:2007PhyA..377..227K. doi:10.1016/j.physa.2006.11.002.
Hernández-Acosta, M. A.; Trejo-Valdez, M.; Castro-Chacón, J. H.; Miguel, C. R. Torres-San; Martínez-Gutiérrez, H. Chaotic signatures of photoconductive Cu 2 ZnSnS 4 nanostructures explored by Lorenz attractors. New Journal of Physics. 2018, 20 (2): 023048. Bibcode:2018NJPh...20b3048H. ISSN 1367-2630. doi:10.1088/1367-2630/aaad41  （英语）.
Hristu-Varsakelis, D.; Kyrtsou, C. Evidence for nonlinear asymmetric causality in US inflation, metal and stock returns. Discrete Dynamics in Nature and Society. 2008, 2008: 1–7. doi:10.1155/2008/138547 . 138547.
Kyrtsou, C.; M. Terraza. Is it possible to study chaotic and ARCH behaviour jointly? Application of a noisy Mackey-Glass equation with heteroskedastic errors to the Paris Stock Exchange returns series. Computational Economics. 2003, 21 (3): 257–276. S2CID 154202123. doi:10.1023/A:1023939610962.
Hubler, A.; Phelps, K. Guiding a self-adjusting system through chaos. Complexity. 2007, 13 (2): 62. Bibcode:2007Cmplx..13b..62W. doi:10.1002/cplx.20204.
Gerig, A. Chaos in a one-dimensional compressible flow. Physical Review E. 2007, 75 (4): 045202. Bibcode:2007PhRvE..75d5202G. PMID 17500951. S2CID 45804559. arXiv:nlin/0701050 . doi:10.1103/PhysRevE.75.045202.
Wotherspoon, T.; Hubler, A. Adaptation to the Edge of Chaos in the Self-Adjusting Logistic Map. The Journal of Physical Chemistry A. 2009, 113 (1): 19–22. Bibcode:2009JPCA..113...19W. PMID 19072712. doi:10.1021/jp804420g.
Borodkin, Leonid I. Challenges of Instability: The Concepts of Synergetics in Studying the Historical Development of Russia. Ural Historical Journal. 2019, 63 (2): 127–136. doi:10.30759/1728-9718-2019-2(63)-127-136 .
Dilão, R.; Domingos, T. Periodic and Quasi-Periodic Behavior in Resource Dependent Age Structured Population Models. Bulletin of Mathematical Biology. 2001, 63 (2): 207–230. PMID 11276524. S2CID 697164. doi:10.1006/bulm.2000.0213.
Akhavan, A.; Samsudin, A.; Akhshani, A. A symmetric image encryption scheme based on combination of nonlinear chaotic maps. Journal of the Franklin Institute. 2011-10-01, 348 (8): 1797–1813. doi:10.1016/j.jfranklin.2011.05.001.
Behnia, S.; Akhshani, A.; Mahmodi, H.; Akhavan, A. A novel algorithm for image encryption based on mixture of chaotic maps. Chaos, Solitons & Fractals. 2008-01-01, 35 (2): 408–419. Bibcode:2008CSF....35..408B. doi:10.1016/j.chaos.2006.05.011.
Wang, Xingyuan; Zhao, Jianfeng. An improved key agreement protocol based on chaos. Commun. Nonlinear Sci. Numer. Simul. 2012, 15 (12): 4052–4057. Bibcode:2010CNSNS..15.4052W. doi:10.1016/j.cnsns.2010.02.014.
Babaei, Majid. A novel text and image encryption method based on chaos theory and DNA computing. Natural Computing. 2013, 12 (1): 101–107. S2CID 18407251. doi:10.1007/s11047-012-9334-9.
Akhavan, A.; Samsudin, A.; Akhshani, A. Cryptanalysis of an image encryption algorithm based on DNA encoding. Optics & Laser Technology. 2017-10-01, 95: 94–99. Bibcode:2017OptLT..95...94A. doi:10.1016/j.optlastec.2017.04.022.
Xu, Ming. Cryptanalysis of an Image Encryption Algorithm Based on DNA Sequence Operation and Hyper-chaotic System. 3D Research. 2017-06-01, 8 (2): 15. Bibcode:2017TDR.....8..126X. ISSN 2092-6731. S2CID 125169427. doi:10.1007/s13319-017-0126-y （英语）.
Liu, Yuansheng; Tang, Jie; Xie, Tao. Cryptanalyzing a RGB image encryption algorithm based on DNA encoding and chaos map. Optics & Laser Technology. 2014-08-01, 60: 111–115. Bibcode:2014OptLT..60..111L. S2CID 18740000. arXiv:1307.4279 . doi:10.1016/j.optlastec.2014.01.015.
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Goswami, Ambarish; Thuilot, Benoit; Espiau, Bernard. A Study of the Passive Gait of a Compass-Like Biped Robot: Symmetry and Chaos. The International Journal of Robotics Research. 1998, 17 (12): 1282–1301. CiteSeerX 10.1.1.17.4861 . S2CID 1283494. doi:10.1177/027836499801701202.
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Lai, Dejian. Comparison study of AR models on the Canadian lynx data: a close look at BDS statistic. Computational Statistics & Data Analysis. 1996, 22 (4): 409–423. doi:10.1016/0167-9473(95)00056-9.
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Bozóki, Zsolt. Chaos theory and power spectrum analysis in computerized cardiotocography. European Journal of Obstetrics & Gynecology and Reproductive Biology. February 1997, 71 (2): 163–168. PMID 9138960. doi:10.1016/s0301-2115(96)02628-0.
Perry, Joe; Smith, Robert; Woiwod, Ian; Morse, David. Perry, Joe N; Smith, Robert H; Woiwod, Ian P; Morse, David R , 编. Chaos in Real Data : The Analysis of Non-Linear Dynamics from Short Ecological Time Series. Population and Community Biology Series 1. Springer Science+Business Media Dordrecht. 2000: xii+226. ISBN 978-94-010-5772-1. S2CID 37855255. doi:10.1007/978-94-011-4010-2.
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Jones, Gareth. Jones, D. Gareth , 编. The Epidemiology of Plant Diseases 1. Springer Science+Business Media Dordrecht. 1998: xvi + 460 + 26 b/w ill. + 33 color ill. ISBN 978-94-017-3302-1. S2CID 1793087. doi:10.1007/978-94-017-3302-1 （英语）.
Juárez, Fernando. Applying the theory of chaos and a complex model of health to establish relations among financial indicators. Procedia Computer Science. 2011, 3: 982–986. doi:10.1016/j.procs.2010.12.161 .
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Orlando, Giuseppe; Zimatore, Giovanna. RQA correlations on real business cycles time series. Indian Academy of Sciences – Conference Series. 2017-12-18, 1 (1): 35–41. doi:10.29195/iascs.01.01.0009 .
Orlando, Giuseppe; Zimatore, Giovanna. Recurrence quantification analysis of business cycles. Chaos, Solitons & Fractals. 2018-05-01, 110: 82–94 [2023-11-15]. Bibcode:2018CSF...110...82O. ISSN 0960-0779. S2CID 85526993. doi:10.1016/j.chaos.2018.02.032. （原始内容存档于2022-12-17）（英语）.
Orlando, Giuseppe; Zimatore, Giovanna. Business cycle modeling between financial crises and black swans: Ornstein–Uhlenbeck stochastic process vs Kaldor deterministic chaotic model. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2020-08-01, 30 (8): 083129 [2023-11-15]. Bibcode:2020Chaos..30h3129O. PMID 32872798. S2CID 235909725. doi:10.1063/5.0015916. （原始内容存档于2022-12-17）.
Li, Mengshan; Xingyuan Huanga; Hesheng Liua; Bingxiang Liub; Yan Wub; Aihua Xiongc; Tianwen Dong. Prediction of gas solubility in polymers by back propagation artificial neural network based on self-adaptive particle swarm optimization algorithm and chaos theory. Fluid Phase Equilibria. 25 October 2013, 356: 11–17. doi:10.1016/j.fluid.2013.07.017.
Morbidelli, A. Chaotic diffusion in celestial mechanics. Regular & Chaotic Dynamics. 2001, 6 (4): 339–353. doi:10.1070/rd2001v006n04abeh000182.
Dingqi, Li; Yuanping Chenga; Lei Wanga; Haifeng Wanga; Liang Wanga; Hongxing Zhou. Prediction method for risks of coal and gas outbursts based on spatial chaos theory using gas desorption index of drill cuttings. Mining Science and Technology. May 2011, 21 (3): 439–443. Bibcode:2011MiSTC..21..439L. doi:10.1016/j.mstc.2011.05.010.

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Bellissard, J.; Bohigas, O.; Casati, G.; Shepelyansky, D.L. A pioneer of chaos. Physica D: Nonlinear Phenomena. 1 July 1999, 131 (1–4): viii–xv. Bibcode:1999PhyD..131D...8B. ISSN 0167-2789. S2CID 119107150. doi:10.1016/s0167-2789(99)90007-6.

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Applying Chaos Theory to Embedded Applications. （原始内容存档于2011-08-09）.

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What is Chaos Theory? – Fractal Foundation. [2019-11-24]. （原始内容存档于2023-09-13）（美国英语）.

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Kiel, L.; Elliott, Euel (编). Chaos Theory in the Social Sciences: Foundations and Applications. Ann Arbor, MI: University of Michigan Press. 1996. ISBN 9780472106387. doi:10.3998/mpub.14623. hdl:2027/fulcrum.d504rm03n （英语）.

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Kolmogorov, Andrey Nikolaevich. Local structure of turbulence in an incompressible fluid for very large Reynolds numbers. Doklady Akademii Nauk SSSR. 1941, 30 (4): 301–5. Bibcode:1941DoSSR..30..301K. Reprinted in: Kolmogorov, A. N. The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers. Proceedings of the Royal Society A. 1991, 434 (1890): 9–13. Bibcode:1991RSPSA.434....9K. S2CID 123612939. doi:10.1098/rspa.1991.0075.
Kolmogorov, A. N. On degeneration of isotropic turbulence in an incompressible viscous liquid. Doklady Akademii Nauk SSSR. 1941, 31 (6): 538–540. Reprinted in: Kolmogorov, A. N. Dissipation of Energy in the Locally Isotropic Turbulence. Proceedings of the Royal Society A. 1991, 434 (1890): 15–17. Bibcode:1991RSPSA.434...15K. S2CID 122060992. doi:10.1098/rspa.1991.0076.
Kolmogorov, A. N. Preservation of conditionally periodic movements with small change in the Hamilton function. Stochastic Behavior in Classical and Quantum Hamiltonian Systems. Lecture Notes in Physics 98. 1979: 527–530. Bibcode:1979LNP....93...51K. ISBN 978-3-540-09120-2. doi:10.1007/BFb0021737. |journal=被忽略 (帮助) See also Kolmogorov–Arnold–Moser theorem
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Musielak, Dora E.; Musielak, Zdzislaw E.; Kennamer, Kenny S. The onset of chaos in nonlinear dynamical systems determined with a new fractal technique. Fractals. 2005-03-01, 13 (1): 19–31 [2023-11-14]. ISSN 0218-348X. doi:10.1142/S0218348X0500274X. （原始内容存档于2023-06-03）.

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