Lyapunov exponent (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Lyapunov exponent" in English language version.

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15doi.org

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arxiv.org

Kuznetsov, N.V. (2016). "The Lyapunov dimension and its estimation via the Leonov method". Physics Letters A. 380 (25–26): 2142–2149. arXiv:1602.05410. Bibcode:2016PhLA..380.2142K. doi:10.1016/j.physleta.2016.04.036. S2CID 118467839.
Kuznetsov, N.V.; Alexeeva, T.A.; Leonov, G.A. (2016). "Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations". Nonlinear Dynamics. 85 (1): 195–201. arXiv:1410.2016. Bibcode:2016NonDy..85..195K. doi:10.1007/s11071-016-2678-4. S2CID 119650438.

doi.org

N.V. Kuznetsov; G.A. Leonov (2005). "On stability by the first approximation for discrete systems". Proceedings. 2005 International Conference Physics and Control, 2005 (PDF). Vol. Proceedings Volume 2005. pp. 596–599. doi:10.1109/PHYCON.2005.1514053. ISBN 978-0-7803-9235-9. S2CID 31746738.
G.A. Leonov; N.V. Kuznetsov (2007). "Time-Varying Linearization and the Perron effects" (PDF). International Journal of Bifurcation and Chaos. 17 (4): 1079–1107. Bibcode:2007IJBC...17.1079L. CiteSeerX 10.1.1.660.43. doi:10.1142/S0218127407017732.
Pesin, Y. B. (1977). "Characteristic Lyapunov Exponents and Smooth Ergodic Theory". Russian Math. Surveys. 32 (4): 55–114. Bibcode:1977RuMaS..32...55P. doi:10.1070/RM1977v032n04ABEH001639. S2CID 250877457.
Kuznetsov, N.V. (2016). "The Lyapunov dimension and its estimation via the Leonov method". Physics Letters A. 380 (25–26): 2142–2149. arXiv:1602.05410. Bibcode:2016PhLA..380.2142K. doi:10.1016/j.physleta.2016.04.036. S2CID 118467839.
Kuznetsov, N.V.; Alexeeva, T.A.; Leonov, G.A. (2016). "Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations". Nonlinear Dynamics. 85 (1): 195–201. arXiv:1410.2016. Bibcode:2016NonDy..85..195K. doi:10.1007/s11071-016-2678-4. S2CID 119650438.
Miller, R. H. (1964). "Irreversibility in Small Stellar Dynamical Systems". The Astrophysical Journal. 140: 250. Bibcode:1964ApJ...140..250M. doi:10.1086/147911.
Benettin, G.; Galgani, L.; Giorgilli, A.; Strelcyn, J. M. (1980). "Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory". Meccanica. 15: 9–20. doi:10.1007/BF02128236. S2CID 123085922.
Benettin, G.; Galgani, L.; Giorgilli, A.; Strelcyn, J. M. (1980). "Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; A method for computing all of them. Part 2: Numerical application". Meccanica. 15: 21–30. doi:10.1007/BF02128237. S2CID 117095512.
Shimada, I.; Nagashima, T. (1979). "A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems". Progress of Theoretical Physics. 61 (6): 1605–1616. Bibcode:1979PThPh..61.1605S. doi:10.1143/PTP.61.1605.
Eckmann, J. -P.; Ruelle, D. (1985). "Ergodic theory of chaos and strange attractors". Reviews of Modern Physics. 57 (3): 617–656. Bibcode:1985RvMP...57..617E. doi:10.1103/RevModPhys.57.617. S2CID 18330392.
Bryant, P.; Brown, R.; Abarbanel, H. (1990). "Lyapunov exponents from observed time series". Physical Review Letters. 65 (13): 1523–1526. Bibcode:1990PhRvL..65.1523B. doi:10.1103/PhysRevLett.65.1523. PMID 10042292.
Brown, R.; Bryant, P.; Abarbanel, H. (1991). "Computing the Lyapunov spectrum of a dynamical system from an observed time series". Physical Review A. 43 (6): 2787–2806. Bibcode:1991PhRvA..43.2787B. doi:10.1103/PhysRevA.43.2787. PMID 9905344.
Bryant, P. H. (1993). "Extensional singularity dimensions for strange attractors". Physics Letters A. 179 (3): 186–190. Bibcode:1993PhLA..179..186B. doi:10.1016/0375-9601(93)91136-S.
Abarbanel, H.D.I.; Brown, R.; Kennel, M.B. (1992). "Local Lyapunov exponents computed from observed data". Journal of Nonlinear Science. 2 (3): 343–365. Bibcode:1992JNS.....2..343A. doi:10.1007/BF01208929. S2CID 122542761.
See, e.g., Pecora, L. M.; Carroll, T. L.; Johnson, G. A.; Mar, D. J.; Heagy, J. F. (1997). "Fundamentals of synchronization in chaotic systems, concepts, and applications". Chaos: An Interdisciplinary Journal of Nonlinear Science. 7 (4): 520–543. Bibcode:1997Chaos...7..520P. doi:10.1063/1.166278. PMID 12779679.

harvard.edu

ui.adsabs.harvard.edu

G.A. Leonov; N.V. Kuznetsov (2007). "Time-Varying Linearization and the Perron effects" (PDF). International Journal of Bifurcation and Chaos. 17 (4): 1079–1107. Bibcode:2007IJBC...17.1079L. CiteSeerX 10.1.1.660.43. doi:10.1142/S0218127407017732.
Pesin, Y. B. (1977). "Characteristic Lyapunov Exponents and Smooth Ergodic Theory". Russian Math. Surveys. 32 (4): 55–114. Bibcode:1977RuMaS..32...55P. doi:10.1070/RM1977v032n04ABEH001639. S2CID 250877457.
Kuznetsov, N.V. (2016). "The Lyapunov dimension and its estimation via the Leonov method". Physics Letters A. 380 (25–26): 2142–2149. arXiv:1602.05410. Bibcode:2016PhLA..380.2142K. doi:10.1016/j.physleta.2016.04.036. S2CID 118467839.
Kuznetsov, N.V.; Alexeeva, T.A.; Leonov, G.A. (2016). "Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations". Nonlinear Dynamics. 85 (1): 195–201. arXiv:1410.2016. Bibcode:2016NonDy..85..195K. doi:10.1007/s11071-016-2678-4. S2CID 119650438.
Miller, R. H. (1964). "Irreversibility in Small Stellar Dynamical Systems". The Astrophysical Journal. 140: 250. Bibcode:1964ApJ...140..250M. doi:10.1086/147911.
Shimada, I.; Nagashima, T. (1979). "A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems". Progress of Theoretical Physics. 61 (6): 1605–1616. Bibcode:1979PThPh..61.1605S. doi:10.1143/PTP.61.1605.
Eckmann, J. -P.; Ruelle, D. (1985). "Ergodic theory of chaos and strange attractors". Reviews of Modern Physics. 57 (3): 617–656. Bibcode:1985RvMP...57..617E. doi:10.1103/RevModPhys.57.617. S2CID 18330392.
Bryant, P.; Brown, R.; Abarbanel, H. (1990). "Lyapunov exponents from observed time series". Physical Review Letters. 65 (13): 1523–1526. Bibcode:1990PhRvL..65.1523B. doi:10.1103/PhysRevLett.65.1523. PMID 10042292.
Brown, R.; Bryant, P.; Abarbanel, H. (1991). "Computing the Lyapunov spectrum of a dynamical system from an observed time series". Physical Review A. 43 (6): 2787–2806. Bibcode:1991PhRvA..43.2787B. doi:10.1103/PhysRevA.43.2787. PMID 9905344.
Bryant, P. H. (1993). "Extensional singularity dimensions for strange attractors". Physics Letters A. 179 (3): 186–190. Bibcode:1993PhLA..179..186B. doi:10.1016/0375-9601(93)91136-S.
Abarbanel, H.D.I.; Brown, R.; Kennel, M.B. (1992). "Local Lyapunov exponents computed from observed data". Journal of Nonlinear Science. 2 (3): 343–365. Bibcode:1992JNS.....2..343A. doi:10.1007/BF01208929. S2CID 122542761.
See, e.g., Pecora, L. M.; Carroll, T. L.; Johnson, G. A.; Mar, D. J.; Heagy, J. F. (1997). "Fundamentals of synchronization in chaotic systems, concepts, and applications". Chaos: An Interdisciplinary Journal of Nonlinear Science. 7 (4): 520–543. Bibcode:1997Chaos...7..520P. doi:10.1063/1.166278. PMID 12779679.

nih.gov

pubmed.ncbi.nlm.nih.gov

Bryant, P.; Brown, R.; Abarbanel, H. (1990). "Lyapunov exponents from observed time series". Physical Review Letters. 65 (13): 1523–1526. Bibcode:1990PhRvL..65.1523B. doi:10.1103/PhysRevLett.65.1523. PMID 10042292.
Brown, R.; Bryant, P.; Abarbanel, H. (1991). "Computing the Lyapunov spectrum of a dynamical system from an observed time series". Physical Review A. 43 (6): 2787–2806. Bibcode:1991PhRvA..43.2787B. doi:10.1103/PhysRevA.43.2787. PMID 9905344.
See, e.g., Pecora, L. M.; Carroll, T. L.; Johnson, G. A.; Mar, D. J.; Heagy, J. F. (1997). "Fundamentals of synchronization in chaotic systems, concepts, and applications". Chaos: An Interdisciplinary Journal of Nonlinear Science. 7 (4): 520–543. Bibcode:1997Chaos...7..520P. doi:10.1063/1.166278. PMID 12779679.

psu.edu

citeseerx.ist.psu.edu

G.A. Leonov; N.V. Kuznetsov (2007). "Time-Varying Linearization and the Perron effects" (PDF). International Journal of Bifurcation and Chaos. 17 (4): 1079–1107. Bibcode:2007IJBC...17.1079L. CiteSeerX 10.1.1.660.43. doi:10.1142/S0218127407017732.

semanticscholar.org

api.semanticscholar.org

N.V. Kuznetsov; G.A. Leonov (2005). "On stability by the first approximation for discrete systems". Proceedings. 2005 International Conference Physics and Control, 2005 (PDF). Vol. Proceedings Volume 2005. pp. 596–599. doi:10.1109/PHYCON.2005.1514053. ISBN 978-0-7803-9235-9. S2CID 31746738.
Pesin, Y. B. (1977). "Characteristic Lyapunov Exponents and Smooth Ergodic Theory". Russian Math. Surveys. 32 (4): 55–114. Bibcode:1977RuMaS..32...55P. doi:10.1070/RM1977v032n04ABEH001639. S2CID 250877457.
Kuznetsov, N.V. (2016). "The Lyapunov dimension and its estimation via the Leonov method". Physics Letters A. 380 (25–26): 2142–2149. arXiv:1602.05410. Bibcode:2016PhLA..380.2142K. doi:10.1016/j.physleta.2016.04.036. S2CID 118467839.
Kuznetsov, N.V.; Alexeeva, T.A.; Leonov, G.A. (2016). "Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations". Nonlinear Dynamics. 85 (1): 195–201. arXiv:1410.2016. Bibcode:2016NonDy..85..195K. doi:10.1007/s11071-016-2678-4. S2CID 119650438.
Benettin, G.; Galgani, L.; Giorgilli, A.; Strelcyn, J. M. (1980). "Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory". Meccanica. 15: 9–20. doi:10.1007/BF02128236. S2CID 123085922.
Benettin, G.; Galgani, L.; Giorgilli, A.; Strelcyn, J. M. (1980). "Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; A method for computing all of them. Part 2: Numerical application". Meccanica. 15: 21–30. doi:10.1007/BF02128237. S2CID 117095512.
Eckmann, J. -P.; Ruelle, D. (1985). "Ergodic theory of chaos and strange attractors". Reviews of Modern Physics. 57 (3): 617–656. Bibcode:1985RvMP...57..617E. doi:10.1103/RevModPhys.57.617. S2CID 18330392.
Abarbanel, H.D.I.; Brown, R.; Kennel, M.B. (1992). "Local Lyapunov exponents computed from observed data". Journal of Nonlinear Science. 2 (3): 343–365. Bibcode:1992JNS.....2..343A. doi:10.1007/BF01208929. S2CID 122542761.

sites.google.com

Tomo, Nakamura (19 October 2022). "nonlinear systems and Lyapunov spectrum".

spbu.ru

math.spbu.ru

N.V. Kuznetsov; G.A. Leonov (2005). "On stability by the first approximation for discrete systems". Proceedings. 2005 International Conference Physics and Control, 2005 (PDF). Vol. Proceedings Volume 2005. pp. 596–599. doi:10.1109/PHYCON.2005.1514053. ISBN 978-0-7803-9235-9. S2CID 31746738.
G.A. Leonov; N.V. Kuznetsov (2007). "Time-Varying Linearization and the Perron effects" (PDF). International Journal of Bifurcation and Chaos. 17 (4): 1079–1107. Bibcode:2007IJBC...17.1079L. CiteSeerX 10.1.1.660.43. doi:10.1142/S0218127407017732.

springer.com

Kuznetsov, Nikolay; Reitmann, Volker (2020). Attractor Dimension Estimates for Dynamical Systems: Theory and Computation. Cham: Springer.

wisc.edu

sprott.physics.wisc.edu

Sprott, Julien Clinton (May 26, 2005). "Lyapunov Exponent Spectrum Software".
Sprott, Julien Clinton (October 4, 2006). "Lyapunov Exponents for Delay Differential Equations".