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Volumn 10, Issue 2-3, 2008, Pages 511-536

High-precision computations of divergent asymptotic series and homoclinic phenomena

Author keywords

High precision computation; Homoclinic orbit; Standard map

Indexed keywords


EID: 67049112335     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2008.10.511     Document Type: Article
Times cited : (29)

References (12)
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  • 3
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    • Singular separatrix splitting and the Melnikov method: An experimental study
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    • Delshams, A.1    Ramírez-Ros, R.2
  • 4
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    • The splitting of separatrices for analytic diffeomorphisms
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    • Fontich, E.1    Simó, C.2
  • 5
    • 0001327147 scopus 로고
    • Exponentially small splittings in Hamiltonian systems
    • V. Gelfreich, V. Lazutkin and M. Tabanov, Exponentially small splittings in Hamiltonian systems, Chaos, 1 (1991), 137-142.
    • (1991) Chaos , vol.1 , pp. 137-142
    • Gelfreich, V.1    Lazutkin, V.2    Tabanov, M.3
  • 6
    • 0033241455 scopus 로고    scopus 로고
    • A proof of the exponentially small transversality of the separatrices for the standard map
    • V. G. Gelfreich, A proof of the exponentially small transversality of the separatrices for the standard map, Comm. Math. Phys., 201 (1999), 155-216.
    • (1999) Comm. Math. Phys. , vol.201 , pp. 155-216
    • Gelfreich, V.G.1
  • 7
    • 0035600465 scopus 로고    scopus 로고
    • Splitting of separatrices: Perturbation theory and exponential smallness
    • V. Gelfreich and V. Lazutkin, Splitting of separatrices: perturbation theory and exponential smallness, Russian Math. Surveys, 56 (2001), 499-558.
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    • Gelfreich, V.1    Lazutkin, V.2
  • 8
    • 21544480029 scopus 로고    scopus 로고
    • Splitting of separatrices for the Chirikov standard map
    • translated from the Russian manuscript originally published in VINITI 1984
    • V. F. Lazutkin, Splitting of separatrices for the Chirikov standard map, J. Math. Sci., 128 (2005), 2687-2705, (translated from the Russian manuscript originally published in VINITI 1984).
    • (2005) J. Math. Sci. , vol.128 , pp. 2687-2705
    • Lazutkin, V.F.1
  • 9
    • 25144476259 scopus 로고    scopus 로고
    • Exponentially small separatrix splittings and almost invisible homoclinic bifurcations in some billiard tables
    • R. Ramírez-Ros, Exponentially small separatrix splittings and almost invisible homoclinic bifurcations in some billiard tables, Phys. D, 210 (2005), 149-179.
    • (2005) Phys. D , vol.210 , pp. 149-179
    • Ramírez-Ros, R.1
  • 10
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    • Melnikȯv's method and averaging
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  • 11
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    • Analytical and numerical detection of exponentially small phenomena
    • Berlin, 1999, World Sci. Publ
    • C. Simó, Analytical and numerical detection of exponentially small phenomena, Equadiff 1999, Vol.1, 2 (Berlin, 1999), 967-976, World Sci. Publ.
    • (1999) Equadiff , vol.1 , Issue.2 , pp. 967-976
    • Simó, C.1
  • 12
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    • Some relevant aspects of area preserving maps and the planar conservative Hénon map
    • Univ. Barcelona
    • C. Simó and A. Vieiro, Some relevant aspects of area preserving maps and the planar conservative Hénon map, Work in progress (2007), Univ. Barcelona.
    • (2007) Work in Progress
    • Simó, C.1    Vieiro, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.