Arnold diffusion (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Arnold diffusion" in English language version.

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12doi.org

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8worldcat.org

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ams.org

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Chierchia, Luigi; Gallavotti, Giovanni (1994). "Drift and diffusion in phase space". Annales de l'I.H.P.: Physique Théorique. 60: 1–144. MR 1259103. Zbl 1010.37039. (Erratum: [Annales de l'I.H.P.: Physique Théorique. 68: 135 (1998)]. If the erratum has been checked and does not affect the cited material, please replace {{erratum|...}} with {{erratum|...|checked=yes}}.)

arxiv.org

Chen, Qinbo; de la Llave, Rafael (2022-03-09). "Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems". Nonlinearity. 35 (4). IOP Publishing: 1986–2019. arXiv:2103.03847. Bibcode:2022Nonli..35.1986C. doi:10.1088/1361-6544/ac50bb. ISSN 0951-7715.
Gidea, Marian; Llave, Rafael; M-Seara, Tere (2019-07-24). "A General Mechanism of Diffusion in Hamiltonian Systems: Qualitative Results". Communications on Pure and Applied Mathematics. 73 (1). Wiley: 150–209. arXiv:1405.0866. doi:10.1002/cpa.21856. hdl:2117/188944. ISSN 0010-3640. S2CID 119150120.
Cheng, Chong-Qing (2019). "The genericity of Arnold diffusion in nearly integrable Hamiltonian systems". Asian Journal of Mathematics. 23 (3). International Press of Boston: 401–438. arXiv:1801.02921. doi:10.4310/ajm.2019.v23.n3.a3. ISSN 1093-6106. S2CID 119677951.

books.google.com

Florin Diacu; Philip Holmes (1996). Celestial Encounters: The Origins of Chaos and Stability. Princeton University Press. p. 193. ISBN 0-691-00545-1.

doi.org

Chen, Qinbo; de la Llave, Rafael (2022-03-09). "Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems". Nonlinearity. 35 (4). IOP Publishing: 1986–2019. arXiv:2103.03847. Bibcode:2022Nonli..35.1986C. doi:10.1088/1361-6544/ac50bb. ISSN 0951-7715.
Mather, John N. (2012). "Arnold Diffusion by Variational Methods". Essays in Mathematics and its Applications. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 271–285. doi:10.1007/978-3-642-28821-0_11. ISBN 978-3-642-28820-3.
Bolotin, S; Treschev, D (1999-01-01). "Unbounded growth of energy in nonautonomous Hamiltonian systems". Nonlinearity. 12 (2). IOP Publishing: 365–388. Bibcode:1999Nonli..12..365B. doi:10.1088/0951-7715/12/2/013. ISSN 0951-7715. S2CID 250852828.
Cheng, Chong-Qing; Yan, Jun (2004-07-01). "Existence of Diffusion Orbits in a priori Unstable Hamiltonian Systems". Journal of Differential Geometry. 67 (3). International Press of Boston. doi:10.4310/jdg/1102091356. ISSN 0022-040X.
Delshams, Amadeu; de la Llave, Rafael; M-Seara, Tere (2006). "A geometric mechanism for diffusion in Hamiltonian systems overcoming in the large gap problem: Heuristics and rigorous verification on a model". Mem. Am. Math. Soc. 179 (844). doi:10.1090/memo/0844. hdl:2117/872.
Gelfreich, Vassili; Turaev, Dmitry (2017-04-24). "Arnold Diffusion in A Priori Chaotic Symplectic Maps" (PDF). Communications in Mathematical Physics. 353 (2). Springer Science and Business Media LLC: 507–547. Bibcode:2017CMaPh.353..507G. doi:10.1007/s00220-017-2867-0. hdl:10044/1/44044. ISSN 0010-3616. S2CID 253744630.
Gidea, Marian; Llave, Rafael; M-Seara, Tere (2019-07-24). "A General Mechanism of Diffusion in Hamiltonian Systems: Qualitative Results". Communications on Pure and Applied Mathematics. 73 (1). Wiley: 150–209. arXiv:1405.0866. doi:10.1002/cpa.21856. hdl:2117/188944. ISSN 0010-3640. S2CID 119150120.
Cheng, Chong-Qing (2019). "The genericity of Arnold diffusion in nearly integrable Hamiltonian systems". Asian Journal of Mathematics. 23 (3). International Press of Boston: 401–438. arXiv:1801.02921. doi:10.4310/ajm.2019.v23.n3.a3. ISSN 1093-6106. S2CID 119677951.
Kaloshin, Vadim; Zhang, Ke (2020-11-12). Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom (PDF). Princeton University Press. doi:10.1515/9780691204932. ISBN 978-0-691-20493-2.
Xia, Zhihong (1993). "Arnold diffusion in the elliptic restricted three-body problem". Journal of Dynamics and Differential Equations. 5 (2). Springer Science and Business Media LLC: 219–240. Bibcode:1993JDDE....5..219X. doi:10.1007/bf01053161. ISSN 1040-7294. S2CID 121370238.
Delshams, Amadeu; Kaloshin, Vadim; de la Rosa, Abraham; Seara, Tere M. (2018-09-05). "Global Instability in the Restricted Planar Elliptic Three Body Problem". Communications in Mathematical Physics. 366 (3). Springer Science and Business Media LLC: 1173–1228. doi:10.1007/s00220-018-3248-z. hdl:2117/123338. ISSN 0010-3616. S2CID 253752812.
Capiński, Maciej; Gidea, Marian (2021). "A general mechanism of instability in Hamiltonian systems: skipping along a normally hyperbolic invariant manifold". Communications on Pure and Applied Mathematics. doi:10.1002/cpa.22014.

handle.net

hdl.handle.net

Delshams, Amadeu; de la Llave, Rafael; M-Seara, Tere (2006). "A geometric mechanism for diffusion in Hamiltonian systems overcoming in the large gap problem: Heuristics and rigorous verification on a model". Mem. Am. Math. Soc. 179 (844). doi:10.1090/memo/0844. hdl:2117/872.
Gelfreich, Vassili; Turaev, Dmitry (2017-04-24). "Arnold Diffusion in A Priori Chaotic Symplectic Maps" (PDF). Communications in Mathematical Physics. 353 (2). Springer Science and Business Media LLC: 507–547. Bibcode:2017CMaPh.353..507G. doi:10.1007/s00220-017-2867-0. hdl:10044/1/44044. ISSN 0010-3616. S2CID 253744630.
Gidea, Marian; Llave, Rafael; M-Seara, Tere (2019-07-24). "A General Mechanism of Diffusion in Hamiltonian Systems: Qualitative Results". Communications on Pure and Applied Mathematics. 73 (1). Wiley: 150–209. arXiv:1405.0866. doi:10.1002/cpa.21856. hdl:2117/188944. ISSN 0010-3640. S2CID 119150120.
Delshams, Amadeu; Kaloshin, Vadim; de la Rosa, Abraham; Seara, Tere M. (2018-09-05). "Global Instability in the Restricted Planar Elliptic Three Body Problem". Communications in Mathematical Physics. 366 (3). Springer Science and Business Media LLC: 1173–1228. doi:10.1007/s00220-018-3248-z. hdl:2117/123338. ISSN 0010-3616. S2CID 253752812.

harvard.edu

ui.adsabs.harvard.edu

Chen, Qinbo; de la Llave, Rafael (2022-03-09). "Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems". Nonlinearity. 35 (4). IOP Publishing: 1986–2019. arXiv:2103.03847. Bibcode:2022Nonli..35.1986C. doi:10.1088/1361-6544/ac50bb. ISSN 0951-7715.
Bolotin, S; Treschev, D (1999-01-01). "Unbounded growth of energy in nonautonomous Hamiltonian systems". Nonlinearity. 12 (2). IOP Publishing: 365–388. Bibcode:1999Nonli..12..365B. doi:10.1088/0951-7715/12/2/013. ISSN 0951-7715. S2CID 250852828.
Gelfreich, Vassili; Turaev, Dmitry (2017-04-24). "Arnold Diffusion in A Priori Chaotic Symplectic Maps" (PDF). Communications in Mathematical Physics. 353 (2). Springer Science and Business Media LLC: 507–547. Bibcode:2017CMaPh.353..507G. doi:10.1007/s00220-017-2867-0. hdl:10044/1/44044. ISSN 0010-3616. S2CID 253744630.
Xia, Zhihong (1993). "Arnold diffusion in the elliptic restricted three-body problem". Journal of Dynamics and Differential Equations. 5 (2). Springer Science and Business Media LLC: 219–240. Bibcode:1993JDDE....5..219X. doi:10.1007/bf01053161. ISSN 1040-7294. S2CID 121370238.

hbz-nrw.de

digitale-objekte.hbz-nrw.de

Kaloshin, Vadim; Zhang, Ke (2020-11-12). Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom (PDF). Princeton University Press. doi:10.1515/9780691204932. ISBN 978-0-691-20493-2.

imj-prg.fr

webusers.imj-prg.fr

Pierre Lochak, (1999) Arnold diffusion; a compendium of remarks and questions In "Hamiltonian Systems with Three or More Degrees of Freedom" (S’Agar´o, 1995), C. Sim´o, ed, NATO ASI Series C: Math. Phys. Sci., Vol. 533, Kluwer Academic, Dordrecht (1999), 168–183.

mathnet.ru

mi.mathnet.ru

Arnold, Vladimir I. (1964). "Instability of dynamical systems with several degrees of freedom". Soviet Mathematics. 5: 581–585.

numdam.org

Chierchia, Luigi; Gallavotti, Giovanni (1994). "Drift and diffusion in phase space". Annales de l'I.H.P.: Physique Théorique. 60: 1–144. MR 1259103. Zbl 1010.37039. (Erratum: [Annales de l'I.H.P.: Physique Théorique. 68: 135 (1998)]. If the erratum has been checked and does not affect the cited material, please replace {{erratum|...}} with {{erratum|...|checked=yes}}.)

rug.nl

math.rug.nl

Henk W. Broer, Mikhail B. Sevryuk (2007) KAM Theory: quasi-periodicity in dynamical systems In: H.W. Broer, B. Hasselblatt and F. Takens (eds.), Handbook of Dynamical Systems Vol. 3, North-Holland, 2010

semanticscholar.org

api.semanticscholar.org

Bolotin, S; Treschev, D (1999-01-01). "Unbounded growth of energy in nonautonomous Hamiltonian systems". Nonlinearity. 12 (2). IOP Publishing: 365–388. Bibcode:1999Nonli..12..365B. doi:10.1088/0951-7715/12/2/013. ISSN 0951-7715. S2CID 250852828.
Gelfreich, Vassili; Turaev, Dmitry (2017-04-24). "Arnold Diffusion in A Priori Chaotic Symplectic Maps" (PDF). Communications in Mathematical Physics. 353 (2). Springer Science and Business Media LLC: 507–547. Bibcode:2017CMaPh.353..507G. doi:10.1007/s00220-017-2867-0. hdl:10044/1/44044. ISSN 0010-3616. S2CID 253744630.
Gidea, Marian; Llave, Rafael; M-Seara, Tere (2019-07-24). "A General Mechanism of Diffusion in Hamiltonian Systems: Qualitative Results". Communications on Pure and Applied Mathematics. 73 (1). Wiley: 150–209. arXiv:1405.0866. doi:10.1002/cpa.21856. hdl:2117/188944. ISSN 0010-3640. S2CID 119150120.
Cheng, Chong-Qing (2019). "The genericity of Arnold diffusion in nearly integrable Hamiltonian systems". Asian Journal of Mathematics. 23 (3). International Press of Boston: 401–438. arXiv:1801.02921. doi:10.4310/ajm.2019.v23.n3.a3. ISSN 1093-6106. S2CID 119677951.
Xia, Zhihong (1993). "Arnold diffusion in the elliptic restricted three-body problem". Journal of Dynamics and Differential Equations. 5 (2). Springer Science and Business Media LLC: 219–240. Bibcode:1993JDDE....5..219X. doi:10.1007/bf01053161. ISSN 1040-7294. S2CID 121370238.
Delshams, Amadeu; Kaloshin, Vadim; de la Rosa, Abraham; Seara, Tere M. (2018-09-05). "Global Instability in the Restricted Planar Elliptic Three Body Problem". Communications in Mathematical Physics. 366 (3). Springer Science and Business Media LLC: 1173–1228. doi:10.1007/s00220-018-3248-z. hdl:2117/123338. ISSN 0010-3616. S2CID 253752812.

warwick.ac.uk

wrap.warwick.ac.uk

Gelfreich, Vassili; Turaev, Dmitry (2017-04-24). "Arnold Diffusion in A Priori Chaotic Symplectic Maps" (PDF). Communications in Mathematical Physics. 353 (2). Springer Science and Business Media LLC: 507–547. Bibcode:2017CMaPh.353..507G. doi:10.1007/s00220-017-2867-0. hdl:10044/1/44044. ISSN 0010-3616. S2CID 253744630.

worldcat.org

search.worldcat.org

Chen, Qinbo; de la Llave, Rafael (2022-03-09). "Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems". Nonlinearity. 35 (4). IOP Publishing: 1986–2019. arXiv:2103.03847. Bibcode:2022Nonli..35.1986C. doi:10.1088/1361-6544/ac50bb. ISSN 0951-7715.
Bolotin, S; Treschev, D (1999-01-01). "Unbounded growth of energy in nonautonomous Hamiltonian systems". Nonlinearity. 12 (2). IOP Publishing: 365–388. Bibcode:1999Nonli..12..365B. doi:10.1088/0951-7715/12/2/013. ISSN 0951-7715. S2CID 250852828.
Cheng, Chong-Qing; Yan, Jun (2004-07-01). "Existence of Diffusion Orbits in a priori Unstable Hamiltonian Systems". Journal of Differential Geometry. 67 (3). International Press of Boston. doi:10.4310/jdg/1102091356. ISSN 0022-040X.
Gelfreich, Vassili; Turaev, Dmitry (2017-04-24). "Arnold Diffusion in A Priori Chaotic Symplectic Maps" (PDF). Communications in Mathematical Physics. 353 (2). Springer Science and Business Media LLC: 507–547. Bibcode:2017CMaPh.353..507G. doi:10.1007/s00220-017-2867-0. hdl:10044/1/44044. ISSN 0010-3616. S2CID 253744630.
Gidea, Marian; Llave, Rafael; M-Seara, Tere (2019-07-24). "A General Mechanism of Diffusion in Hamiltonian Systems: Qualitative Results". Communications on Pure and Applied Mathematics. 73 (1). Wiley: 150–209. arXiv:1405.0866. doi:10.1002/cpa.21856. hdl:2117/188944. ISSN 0010-3640. S2CID 119150120.
Cheng, Chong-Qing (2019). "The genericity of Arnold diffusion in nearly integrable Hamiltonian systems". Asian Journal of Mathematics. 23 (3). International Press of Boston: 401–438. arXiv:1801.02921. doi:10.4310/ajm.2019.v23.n3.a3. ISSN 1093-6106. S2CID 119677951.
Xia, Zhihong (1993). "Arnold diffusion in the elliptic restricted three-body problem". Journal of Dynamics and Differential Equations. 5 (2). Springer Science and Business Media LLC: 219–240. Bibcode:1993JDDE....5..219X. doi:10.1007/bf01053161. ISSN 1040-7294. S2CID 121370238.
Delshams, Amadeu; Kaloshin, Vadim; de la Rosa, Abraham; Seara, Tere M. (2018-09-05). "Global Instability in the Restricted Planar Elliptic Three Body Problem". Communications in Mathematical Physics. 366 (3). Springer Science and Business Media LLC: 1173–1228. doi:10.1007/s00220-018-3248-z. hdl:2117/123338. ISSN 0010-3616. S2CID 253752812.

zbmath.org

Chierchia, Luigi; Gallavotti, Giovanni (1994). "Drift and diffusion in phase space". Annales de l'I.H.P.: Physique Théorique. 60: 1–144. MR 1259103. Zbl 1010.37039. (Erratum: [Annales de l'I.H.P.: Physique Théorique. 68: 135 (1998)]. If the erratum has been checked and does not affect the cited material, please replace {{erratum|...}} with {{erratum|...|checked=yes}}.)