메뉴 건너뛰기




Volumn 15, Issue 2, 2010, Pages 159-164

Universal dynamics in a neighborhood of a generic elliptic periodic point

Author keywords

Area preserving map; Exponentially small splitting; Hamiltonian system; Homoclinic tangency; KAM theory; Newhouse phenomenon; Volume preserving flow; Wild hyperbolic set

Indexed keywords


EID: 77951899662     PISSN: 15603547     EISSN: 14684845     Source Type: Journal    
DOI: 10.1134/S156035471002005X     Document Type: Article
Times cited : (20)

References (16)
  • 1
    • 84980189768 scopus 로고
    • Homoclinic Points Near Elliptic Fixed Points
    • Zehnder, E., Homoclinic Points Near Elliptic Fixed Points, Comm. Pure Appl. Math., 1973, vol. 26, pp. 131-182.
    • (1973) Comm. Pure Appl. Math. , vol.26 , pp. 131-182
    • Zehnder, E.1
  • 2
    • 0242371112 scopus 로고    scopus 로고
    • Polynomial Approximations of Symplectic Dynamics and Richness of Chaos in Non-Hyperbolic Area-Preserving Maps
    • Turaev, D., Polynomial Approximations of Symplectic Dynamics and Richness of Chaos in Non-Hyperbolic Area-Preserving Maps, Nonlinearity, 2003, vol. 16, pp. 123-135.
    • (2003) Nonlinearity , vol.16 , pp. 123-135
    • Turaev, D.1
  • 3
    • 33947622603 scopus 로고    scopus 로고
    • Homoclinic Tangencies of Arbitrarily High Orders in Conservative and Dissipative Two-Dimensional Maps
    • Gonchenko, S., Turaev, D., and Shilnikov, L., Homoclinic Tangencies of Arbitrarily High Orders in Conservative and Dissipative Two-Dimensional Maps, Nonlinearity, 2007, vol. 20, pp. 241-275.
    • (2007) Nonlinearity , vol.20 , pp. 241-275
    • Gonchenko, S.1    Turaev, D.2    Shilnikov, L.3
  • 4
    • 0040639188 scopus 로고    scopus 로고
    • Persistence of Homoclinic Tangencies for Area-Preserving Maps
    • Mora, L. and Romero, N., Persistence of Homoclinic Tangencies for Area-Preserving Maps, Ann. Fac. Sci. Toulouse (6), 1997, vol. 6, no. 4, pp. 711-725.
    • (1997) Ann. Fac. Sci. Toulouse (6) , vol.6 , Issue.4 , pp. 711-725
    • Mora, L.1    Romero, N.2
  • 5
    • 84974069323 scopus 로고
    • From a Differentiable to a Real Analytic Perturbation Theory, Applications to the Kupka-Smale Theorem
    • Broer, H. and Tangerman, F., From a Differentiable to a Real Analytic Perturbation Theory, Applications to the Kupka-Smale Theorem, Ergodic Theory Dynam. Systems, 1986, vol. 6, pp. 345-362.
    • (1986) Ergodic Theory Dynam. Systems , vol.6 , pp. 345-362
    • Broer, H.1    Tangerman, F.2
  • 6
    • 0035600465 scopus 로고    scopus 로고
    • Splitting of Separatrices: Perturbation Theory and Exponential Smallness
    • Gelfreich, V. and Lazutkin, V., Splitting of Separatrices: Perturbation Theory and Exponential Smallness, Russian Math. Surveys, 2001, vol. 56, pp. 499-558.
    • (2001) Russian Math. Surveys , vol.56 , pp. 499-558
    • Gelfreich, V.1    Lazutkin, V.2
  • 7
    • 56549083290 scopus 로고    scopus 로고
    • Elliptic Isles in Families of Area-Preserving Maps
    • Duarte, P., Elliptic Isles in Families of Area-Preserving Maps, Ergodic Theory Dynam. Systems, 2008, vol. 28, no. 6, pp. 1781-1813.
    • (2008) Ergodic Theory Dynam. Systems , vol.28 , Issue.6 , pp. 1781-1813
    • Duarte, P.1
  • 8
    • 51249181043 scopus 로고
    • The Abundance of Wild Hyperbolic Sets and Nonsmooth Stable Sets for Diffeomorphisms
    • Newhouse, S., The Abundance of Wild Hyperbolic Sets and Nonsmooth Stable Sets for Diffeomorphisms, Inst. Hautes' Etudes Sci. Publ. Math., 1979, vol. 50, pp. 101-151.
    • (1979) Inst. Hautes' Etudes Sci. Publ. Math. , vol.50 , pp. 101-151
    • Newhouse, S.1
  • 9
    • 0001128134 scopus 로고
    • Quasi-Elliptic Periodic Points in Conservative Dynamical Systems
    • Newhouse, S., Quasi-Elliptic Periodic Points in Conservative Dynamical Systems, Amer. J. Math., 1977, vol. 99, pp. 1061-1087.
    • (1977) Amer. J. Math. , vol.99 , pp. 1061-1087
    • Newhouse, S.1
  • 10
    • 0000702649 scopus 로고
    • Complex Dynamics and Bifurcations in a Hamiltonian System Having a Transversal Homoclinic Orbit to a Saddle Focus
    • Lerman, L., Complex Dynamics and Bifurcations in a Hamiltonian System Having a Transversal Homoclinic Orbit to a Saddle Focus, Chaos, 1991, vol. 1, no. 2, pp. 174-180.
    • (1991) Chaos , vol.1 , Issue.2 , pp. 174-180
    • Lerman, L.1
  • 11
    • 0042370385 scopus 로고
    • On the Bifurcation of a Saddle-Focus Separatrix Loop in a Three-Dimensional Conservative Dynamical System
    • Biragov, V. and Shilnikov, L., On the Bifurcation of a Saddle-Focus Separatrix Loop in a Three-Dimensional Conservative Dynamical System, Selecta Math. Soviet., 1992, vol. 11, no. 4, pp. 333-340.
    • (1992) Selecta Math. Soviet. , vol.11 , Issue.4 , pp. 333-340
    • Biragov, V.1    Shilnikov, L.2
  • 12
    • 0034287926 scopus 로고    scopus 로고
    • On Two-Dimensional Area-Preserving Diffeomorphisms with Infinitely Many Elliptic Islands
    • Gonchenko, S. and Shilnikov, L., On Two-Dimensional Area-Preserving Diffeomorphisms with Infinitely Many Elliptic Islands, J. Stat. Phys., 2000, vol. 101, pp. 321-356.
    • (2000) J. Stat. Phys. , vol.101 , pp. 321-356
    • Gonchenko, S.1    Shilnikov, L.2
  • 13
    • 17344390264 scopus 로고    scopus 로고
    • Abundance of Elliptic Isles at Conservative Bifurcations
    • Duarte, P., Abundance of Elliptic Isles at Conservative Bifurcations, Dynam. Stability Systems, 1999, vol. 14, no. 4, pp. 339-356.
    • (1999) Dynam. Stability Systems , vol.14 , Issue.4 , pp. 339-356
    • Duarte, P.1
  • 14
    • 73149099359 scopus 로고    scopus 로고
    • Periodic Orbits and Stability Islands in Chaotic Seas Created by Separatrix Crossings in Slow-Fast Systems
    • Neishtadt, A., Simó, C., Treschev, D., and Vasiliev A., Periodic Orbits and Stability Islands in Chaotic Seas Created by Separatrix Crossings in Slow-Fast Systems, Discrete Contin. Dyn. Syst. Ser. B, 2008, vol. 10, pp. 621-650.
    • (2008) Discrete Contin. Dyn. Syst. Ser. B , vol.10 , pp. 621-650
    • Neishtadt, A.1    Simó, C.2    Treschev, D.3    Vasiliev, A.4
  • 15
    • 0007679077 scopus 로고    scopus 로고
    • Islands Appearing in Near-Ergodic Flows
    • Turaev, D. and Rom-Kedar, V., Islands Appearing in Near-Ergodic Flows, Nonlinearity, 1998, vol. 11, pp. 575-600.
    • (1998) Nonlinearity , vol.11 , pp. 575-600
    • Turaev, D.1    Rom-Kedar, V.2
  • 16
    • 0346703292 scopus 로고    scopus 로고
    • Big Islands in Dispersing Billiard-Like Potentials
    • Rom-Kedar, V. and Turaev, D., Big Islands in Dispersing Billiard-Like Potentials, Phys. D, 1999, vol. 130, pp. 187-210.
    • (1999) Phys. D , vol.130 , pp. 187-210
    • Rom-Kedar, V.1    Turaev, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.