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Volumn 267, Issue 1, 2009, Pages 76-90

Conservative homoclinic bifurcations and some applications

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EID: 76049127194     PISSN: 00815438     EISSN: None     Source Type: Journal    
DOI: 10.1134/S0081543809040063     Document Type: Article
Times cited : (5)

References (59)
  • 1
    • 0040177547 scopus 로고
    • Sur l'allure finale du mouvement dans le problème des trois corps
    • Paris: Gauthier-Villars
    • V. M. Alexeyev, "Sur l'allure finale du mouvement dans le problème des trois corps," in Actes Congr. Int. Math., Nice, 1970 (Gauthier-Villars, Paris, 1971), Vol. 2, pp. 893-907.
    • (1971) Actes Congr. Int. Math., Nice, 1970 , pp. 893-907
    • Alexeyev, V.M.1
  • 3
    • 4944255089 scopus 로고    scopus 로고
    • Récurrence et généricité
    • C. Bonatti and S. Crovisier, "Récurrence et généricité," Invent. Math. 158(1), 33-104 (2004).
    • (2004) Invent. Math. , vol.158 , Issue.1 , pp. 33-104
    • Bonatti, C.1    Crovisier, S.2
  • 4
    • 0035648602 scopus 로고    scopus 로고
    • Mushrooms and Other Billiards with Divided Phase Space
    • L. A. Bunimovich, "Mushrooms and Other Billiards with Divided Phase Space," Chaos 11, 802-808 (2001).
    • (2001) Chaos , vol.11 , pp. 802-808
    • Bunimovich, L.A.1
  • 5
    • 54649084411 scopus 로고    scopus 로고
    • On Separatrix Splitting of Some Quadratic Area-Preserving Maps of the Plane
    • V. L. Chernov, "On Separatrix Splitting of Some Quadratic Area-Preserving Maps of the Plane," Regul. Chaotic Dyn. 3(1), 49-65 (1998).
    • (1998) Regul. Chaotic Dyn. , vol.3 , Issue.1 , pp. 49-65
    • Chernov, V.L.1
  • 6
    • 0012097571 scopus 로고
    • A Universal Instability of Many-Dimensional Oscillator Systems
    • B. V. Chirikov, "A Universal Instability of Many-Dimensional Oscillator Systems," Phys. Rep. 52, 263-379 (1979).
    • (1979) Phys. Rep. , vol.52 , pp. 263-379
    • Chirikov, B.V.1
  • 7
    • 0001073501 scopus 로고
    • The Existence of Transverse Homoclinic Points in the Sitnikov Problem
    • H. Dankowicz and P. Holmes, "The Existence of Transverse Homoclinic Points in the Sitnikov Problem," J. Diff. Eqns. 116(2), 468-483 (1995).
    • (1995) J. Diff. Eqns. , vol.116 , Issue.2 , pp. 468-483
    • Dankowicz, H.1    Holmes, P.2
  • 8
    • 84974277538 scopus 로고
    • Geodesic Flow on the Two-Sphere. I: Positive Measure Entropy
    • V. J. Donnay, "Geodesic Flow on the Two-Sphere. I: Positive Measure Entropy," Ergodic Theory Dyn. Syst. 8(4), 531-553 (1988).
    • (1988) Ergodic Theory Dyn. Syst. , vol.8 , Issue.4 , pp. 531-553
    • Donnay, V.J.1
  • 9
    • 18244372671 scopus 로고    scopus 로고
    • Symbolic Extensions and Smooth Dynamical Systems
    • T. Downarowicz and S. Newhouse, "Symbolic Extensions and Smooth Dynamical Systems," Invent. Math. 160(3), 453-499 (2005).
    • (2005) Invent. Math. , vol.160 , Issue.3 , pp. 453-499
    • Downarowicz, T.1    Newhouse, S.2
  • 10
    • 85012297095 scopus 로고
    • Plenty of Elliptic Islands for the Standard Family of Area Preserving Maps
    • P. Duarte, "Plenty of Elliptic Islands for the Standard Family of Area Preserving Maps," Ann. Inst. Henri Poincaré, Anal. Non Linéaire 11(4), 359-409 (1994).
    • (1994) Ann. Inst. Henri Poincaré, Anal. Non Linéaire , vol.11 , Issue.4 , pp. 359-409
    • Duarte, P.1
  • 11
    • 17344390264 scopus 로고    scopus 로고
    • Abundance of Elliptic Isles at Conservative Bifurcations
    • P. Duarte, "Abundance of Elliptic Isles at Conservative Bifurcations," Dyn. Stab. Syst. 14(4), 339-356 (1999).
    • (1999) Dyn. Stab. Syst. , vol.14 , Issue.4 , pp. 339-356
    • Duarte, P.1
  • 12
    • 0034397323 scopus 로고    scopus 로고
    • Persistent Homoclinic Tangencies for Conservative Maps near the Identity
    • P. Duarte, "Persistent Homoclinic Tangencies for Conservative Maps near the Identity," Ergodic Theory Dyn. Syst. 20(2), 393-438 (2000).
    • (2000) Ergodic Theory Dyn. Syst. , vol.20 , Issue.2 , pp. 393-438
    • Duarte, P.1
  • 13
    • 56549083290 scopus 로고    scopus 로고
    • Elliptic Isles in Families of Area-Preserving Maps
    • P. Duarte, "Elliptic Isles in Families of Area-Preserving Maps," Ergodic Theory Dyn. Syst. 28(6), 1781-1813 (2008).
    • (2008) Ergodic Theory Dyn. Syst. , vol.28 , Issue.6 , pp. 1781-1813
    • Duarte, P.1
  • 14
    • 76049109965 scopus 로고
    • On Integrability of Quadratic Area Preserving Mappings in the Plane
    • Lect. Notes Phys, Berlin: Springer
    • E. Fontich, "On Integrability of Quadratic Area Preserving Mappings in the Plane," in Dynamical Systems and Chaos (Springer, Berlin, 1983), Lect. Notes Phys. 179, pp. 270-271.
    • (1983) Dynamical Systems and Chaos , vol.179 , pp. 270-271
    • Fontich, E.1
  • 15
    • 84971996008 scopus 로고
    • The Splitting of Separatrices for Analytic Diffeomorphisms
    • E. Fontich and C. Simó, "The Splitting of Separatrices for Analytic Diffeomorphisms," Ergodic Theory Dyn. Syst. 10(2), 295-318 (1990).
    • (1990) Ergodic Theory Dyn. Syst. , vol.10 , Issue.2 , pp. 295-318
    • Fontich, E.1    Simó, C.2
  • 16
    • 84972004210 scopus 로고
    • Invariant Manifolds for Near Identity Differentiable Maps and Splitting of Separatrices
    • E. Fontich and C. Simó, "Invariant Manifolds for Near Identity Differentiable Maps and Splitting of Separatrices," Ergodic Theory Dyn. Syst. 10(2), 319-346 (1990).
    • (1990) Ergodic Theory Dyn. Syst. , vol.10 , Issue.2 , pp. 319-346
    • Fontich, E.1    Simó, C.2
  • 18
    • 0000563240 scopus 로고    scopus 로고
    • Conjugation to a Shift and the Splitting of Invariant Manifolds
    • V. G. Gelfreich, "Conjugation to a Shift and the Splitting of Invariant Manifolds," Appl. Math. 24(2), 127-140 (1996).
    • (1996) Appl. Math. , vol.24 , Issue.2 , pp. 127-140
    • Gelfreich, V.G.1
  • 19
    • 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," Commun. Math. Phys. 201(1), 155-216 (1999).
    • (1999) Commun. Math. Phys. , vol.201 , Issue.1 , pp. 155-216
    • Gelfreich, V.G.1
  • 20
    • 0005147868 scopus 로고    scopus 로고
    • Splitting of a Small Separatrix Loop near the Saddle-Center Bifurcation in Area-Preserving Maps
    • V. Gelfreich, "Splitting of a Small Separatrix Loop near the Saddle-Center Bifurcation in Area-Preserving Maps," Physica D 136(3-4), 266-279 (2000).
    • (2000) Physica D , vol.136 , Issue.3-4 , pp. 266-279
    • Gelfreich, V.1
  • 21
    • 21544449251 scopus 로고    scopus 로고
    • Splitting of Separatrices: Perturbation Theory and Exponential Smallness
    • [Russ. Math. Surv. 56, 499-558 (2001)]
    • V. G. Gelfreich and V. F. Lazutkin, "Splitting of Separatrices: Perturbation Theory and Exponential Smallness," Usp. Mat. Nauk 56(3), 79-142 (2001) [Russ. Math. Surv. 56, 499-558 (2001)].
    • (2001) Usp. Mat. Nauk , vol.56 , Issue.3 , pp. 79-142
    • Gelfreich, V.G.1    Lazutkin, V.F.2
  • 22
    • 0035612003 scopus 로고    scopus 로고
    • Borel Summation and Splitting of Separatrices for the Hénon Map
    • V. Gelfreich and D. Sauzin, "Borel Summation and Splitting of Separatrices for the Hénon Map," Ann. Inst. Fourier 51(2), 513-567 (2001).
    • (2001) Ann. Inst. Fourier , vol.51 , Issue.2 , pp. 513-567
    • Gelfreich, V.1    Sauzin, D.2
  • 23
    • 32044452038 scopus 로고    scopus 로고
    • On Two-Dimensional Area-Preserving Maps with Homoclinic Tangencies That Have Infinitely Many Generic Elliptic Periodic Points
    • [J. Math. Sci. 128 (2), 2767-2773 (2005)]
    • S. V. Gonchenko and L. P. Shilnikov, "On Two-Dimensional Area-Preserving Maps with Homoclinic Tangencies That Have Infinitely Many Generic Elliptic Periodic Points," Zap. Nauchn. Semin. POMI 300, 155-166 (2003) [J. Math. Sci. 128 (2), 2767-2773 (2005)].
    • (2003) Zap. Nauchn. Semin. POMI , vol.300 , pp. 155-166
    • Gonchenko, S.V.1    Shilnikov, L.P.2
  • 24
    • 33947622603 scopus 로고    scopus 로고
    • Homoclinic Tangencies of Arbitrarily High Orders in Conservative and Dissipative Two-Dimensional Maps
    • S. Gonchenko, D. Turaev, and L. Shilnikov, "Homoclinic Tangencies of Arbitrarily High Orders in Conservative and Dissipative Two-Dimensional Maps," Nonlinearity 20(2), 241-275 (2007).
    • (2007) Nonlinearity , vol.20 , Issue.2 , pp. 241-275
    • Gonchenko, S.1    Turaev, D.2    Shilnikov, L.3
  • 25
    • 0001039322 scopus 로고
    • Numerical Study of Quadratic Area Preserving Mappings
    • M. Hénon, "Numerical Study of Quadratic Area Preserving Mappings," Quart. Appl. Math. 27(3), 291-312 (1969).
    • (1969) Quart. Appl. Math. , vol.27 , Issue.3 , pp. 291-312
    • Hénon, M.1
  • 26
    • 84995319980 scopus 로고
    • Nearly Linear Mappings and Their Applications
    • F. M. Izraelev, "Nearly Linear Mappings and Their Applications," Physica D 1(3), 243-266 (1980).
    • (1980) Physica D , vol.1 , Issue.3 , pp. 243-266
    • Izraelev, F.M.1
  • 27
    • 0034349439 scopus 로고    scopus 로고
    • Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits
    • V. Yu. Kaloshin, "Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits," Commun. Math. Phys. 211(1), 253-271 (2000).
    • (2000) Commun. Math. Phys. , vol.211 , Issue.1 , pp. 253-271
    • Kaloshin, V.Y.1
  • 28
    • 0000118838 scopus 로고
    • Bernoulli Diffeomorphisms on Surfaces
    • A. Katok, "Bernoulli Diffeomorphisms on Surfaces," Ann. Math., Ser. 2, 110(3), 529-547 (1979).
    • (1979) Ann. Math., Ser. 2 , vol.110 , Issue.3 , pp. 529-547
    • Katok, A.1
  • 29
    • 27244458584 scopus 로고    scopus 로고
    • Birth of an Elliptic Island in a Chaotic Sea
    • C. Liverani, "Birth of an Elliptic Island in a Chaotic Sea," Math. Phys. Electron. J. 10, 1 (2004).
    • (2004) Math. Phys. Electron. J. , vol.10 , pp. 1
    • Liverani, C.1
  • 30
    • 0007383374 scopus 로고
    • Oscillatory Solutions in the Planar Restricted Three-Body Problem
    • J. Llibre and C. Simó, "Oscillatory Solutions in the Planar Restricted Three-Body Problem," Math. Ann. 248, 153-184 (1980).
    • (1980) Math. Ann. , vol.248 , pp. 153-184
    • Llibre, J.1    Simó, C.2
  • 31
    • 85013722247 scopus 로고
    • Some Homoclinic Phenomena in the Three Body Problem
    • J. Llibre and C. Simó, "Some Homoclinic Phenomena in the Three Body Problem," J. Diff Eqns. 37, 444-465 (1980).
    • (1980) J. Diff Eqns. , vol.37 , pp. 444-465
    • Llibre, J.1    Simó, C.2
  • 32
    • 84956125562 scopus 로고
    • Hausdorff Dimension for Horseshoes
    • H. McCluskey and A. Manning, "Hausdorff Dimension for Horseshoes," Ergodic Theory Dyn. Syst. 3(2), 251-260 (1983).
    • (1983) Ergodic Theory Dyn. Syst. , vol.3 , Issue.2 , pp. 251-260
    • McCluskey, H.1    Manning, A.2
  • 33
    • 0002007686 scopus 로고
    • A Stable Manifold Theorem for Degenerate Fixed Points with Applications to Celestial Mechanics
    • R. McGehee, "A Stable Manifold Theorem for Degenerate Fixed Points with Applications to Celestial Mechanics," J. Diff. Eqns. 14, 70-88 (1973).
    • (1973) J. Diff. Eqns. , vol.14 , pp. 70-88
    • McGehee, R.1
  • 34
    • 0002238227 scopus 로고    scopus 로고
    • Moser's Invariant Curves and Homoclinic Bifurcations
    • L. Mora and N. Romero, "Moser's Invariant Curves and Homoclinic Bifurcations," Dyn. Syst. Appl. 6, 29-42 (1997).
    • (1997) Dyn. Syst. Appl. , vol.6 , pp. 29-42
    • Mora, L.1    Romero, N.2
  • 35
    • 0242344635 scopus 로고
    • Abundance of Strange Attractors
    • L. Mora and M. Viana, "Abundance of Strange Attractors," Acta Math. 171(1), 1-71 (1993).
    • (1993) Acta Math. , vol.171 , Issue.1 , pp. 1-71
    • Mora, L.1    Viana, M.2
  • 36
    • 0001409680 scopus 로고    scopus 로고
    • Stable Intersections of Cantor Sets and Homoclinic Bifurcations
    • C. G. T. de A. Moreira, "Stable Intersections of Cantor Sets and Homoclinic Bifurcations," Ann. Inst. Henri Poincaré, Anal. Non Linéaire 13(6), 741-781 (1996).
    • (1996) Ann. Inst. Henri Poincaré, Anal. Non Linéaire , vol.13 , Issue.6 , pp. 741-781
    • de Moreira, C.G.T.A.1
  • 38
    • 0000935850 scopus 로고
    • 2
    • Proc. Symp. Pure Math, Providence, RI: Am. Math. Soc
    • 2," in Global Analysis (Am. Math. Soc., Providence, RI, 1970), Proc. Symp. Pure Math. 14, pp. 191-202.
    • (1970) Global Analysis , vol.14 , pp. 191-202
    • Newhouse, S.E.1
  • 39
    • 32044475236 scopus 로고
    • Diffeomorphisms with Infinitely Many Sinks
    • S. E. Newhouse, "Diffeomorphisms with Infinitely Many Sinks," Topology 13, 9-18 (1974).
    • (1974) Topology , vol.13 , pp. 9-18
    • Newhouse, S.E.1
  • 40
    • 0001128134 scopus 로고
    • Quasi-elliptic Periodic Points in Conservative Dynamical Systems
    • S. E. Newhouse, "Quasi-elliptic Periodic Points in Conservative Dynamical Systems," Am. J. Math. 99(5), 1061-1087 (1977).
    • (1977) Am. J. Math. , vol.99 , Issue.5 , pp. 1061-1087
    • Newhouse, S.E.1
  • 41
    • 9344263591 scopus 로고
    • Topological Entropy and Hausdorff Dimension for Area Preserving Diffeomorphisms of Surfaces
    • Paris: Soc. Math. France
    • S. E. Newhouse, "Topological Entropy and Hausdorff Dimension for Area Preserving Diffeomorphisms of Surfaces," in Dynamical Systems, Warsaw, June 27-July 2, 1977 (Soc. Math. France, Paris, 1978), Vol. 3, Astérisque 51, pp. 323-334.
    • (1978) Dynamical Systems, Warsaw, June 27-July 2, 1977 , pp. 323-334
    • Newhouse, S.E.1
  • 42
    • 51249181043 scopus 로고
    • The Abundance of Wild Hyperbolic Sets and Non-smooth Stable Sets for Diffeomorphisms
    • S. E. Newhouse, "The Abundance of Wild Hyperbolic Sets and Non-smooth Stable Sets for Diffeomorphisms," Publ. Math., Inst. Hautes Étud. Sci. 50, 101-151 (1979).
    • (1979) Publ. Math., Inst. Hautes Étud. Sci. , vol.50 , pp. 101-151
    • Newhouse, S.E.1
  • 44
    • 0003377111 scopus 로고
    • Cycles and Bifurcation Theory
    • Paris: Soc. Math. France
    • S. Newhouse and J. Palis, "Cycles and Bifurcation Theory," in Trois études en dynamique qualitative (Soc. Math. France, Paris, 1976), Astérisque 31, pp. 44-140.
    • (1976) Trois études En Dynamique Qualitative , pp. 44-140
    • Newhouse, S.1    Palis, J.2
  • 45
    • 0001526473 scopus 로고
    • Hyperbolicity and the Creation of Homoclinic Orbits
    • J. Palis and F. Takens, "Hyperbolicity and the Creation of Homoclinic Orbits," Ann. Math., Ser. 2, 125(2), 337-374 (1987).
    • (1987) Ann. Math., Ser. 2 , vol.125 , Issue.2 , pp. 337-374
    • Palis, J.1    Takens, F.2
  • 47
    • 0001731090 scopus 로고
    • On the Continuity of Hausdorff Dimension and Limit Capacity for Horseshoes
    • Lect. Notes Math, Berlin: Springer
    • J. Palis and M. Viana, "On the Continuity of Hausdorff Dimension and Limit Capacity for Horseshoes," in Dynamical Systems: Proc. Symp., Valparaiso (Chile), 1986 (Springer, Berlin, 1988), Lect. Notes Math. 1331, pp. 150-160.
    • (1988) Dynamical Systems: Proc. Symp., Valparaiso (Chile), 1986 , vol.1331 , pp. 150-160
    • Palis, J.1    Viana, M.2
  • 49
    • 84961291543 scopus 로고
    • Characteristic Lyapunov Exponents and Smooth Ergodic Theory
    • [Russ. Math. Surv. 32 (4), 55-114 (1977)]
    • Ya. B. Pesin, "Characteristic Lyapunov Exponents and Smooth Ergodic Theory," Usp. Mat. Nauk 32(4), 55-112 (1977) [Russ. Math. Surv. 32 (4), 55-114 (1977)].
    • (1977) Usp. Mat. Nauk , vol.32 , Issue.4 , pp. 55-112
    • Pesin, Y.B.1
  • 50
    • 33745536279 scopus 로고
    • Examples of Conservative Diffeomorphisms of the Two-Dimensional Torus with Coexistence of Elliptic and Stochastic Behavior
    • F. Przytycki, "Examples of Conservative Diffeomorphisms of the Two-Dimensional Torus with Coexistence of Elliptic and Stochastic Behavior," Ergodic Theory Dyn. Syst. 2(3-4), 439-463 (1982).
    • (1982) Ergodic Theory Dyn. Syst. , vol.2 , Issue.3-4 , pp. 439-463
    • Przytycki, F.1
  • 51
    • 0000154315 scopus 로고
    • Bifurcation to Infinitely Many Sinks
    • C. Robinson, "Bifurcation to Infinitely Many Sinks," Commun. Math. Phys. 90(3), 433-459 (1983).
    • (1983) Commun. Math. Phys. , vol.90 , Issue.3 , pp. 433-459
    • Robinson, C.1
  • 52
    • 38249024533 scopus 로고
    • The Existence of Oscillatory and Superhyperbolic Motion in Newtonian Systems
    • D. G. Saari and Z. Xia, "The Existence of Oscillatory and Superhyperbolic Motion in Newtonian Systems," J. Diff. Eqns. 82(2), 342-355 (1989).
    • (1989) J. Diff. Eqns. , vol.82 , Issue.2 , pp. 342-355
    • Saari, D.G.1    Xia, Z.2
  • 54
    • 0004192457 scopus 로고
    • Princeton Math. Ser, Princeton, NJ: Princeton Univ. Press
    • Ya. Sinai, Topics in Ergodic Theory (Princeton Univ. Press, Princeton, NJ, 1994), Princeton Math. Ser. 44.
    • (1994) Topics in Ergodic Theory , vol.44
    • Sinai, Y.1
  • 55
    • 0040427030 scopus 로고
    • The Existence of Oscillatory Motions in the Three-Body Problem
    • [Sov. Phys., Dokl. 5, 647-650 (1960)]
    • K. A. Sitnikov, "The Existence of Oscillatory Motions in the Three-Body Problem," Dokl. Akad. Nauk SSSR 133(2), 303-306 (1960) [Sov. Phys., Dokl. 5, 647-650 (1960)].
    • (1960) Dokl. Akad. Nauk SSSR , vol.133 , Issue.2 , pp. 303-306
    • Sitnikov, K.A.1
  • 56
    • 11944253633 scopus 로고
    • Chaotic Landau Level Mixing in Classical and Quantum Wells
    • D. L. Shepelyansky and A. D. Stone, "Chaotic Landau Level Mixing in Classical and Quantum Wells," Phys. Rev. Lett. 74, 2098-2101 (1995).
    • (1995) Phys. Rev. Lett. , vol.74 , pp. 2098-2101
    • Shepelyansky, D.L.1    Stone, A.D.2
  • 57
    • 0001451552 scopus 로고
    • The Structure of Local Homeomorphisms. III
    • S. Sternberg, "The Structure of Local Homeomorphisms. III," Am. J. Math. 81, 578-604 (1959).
    • (1959) Am. J. Math. , vol.81 , pp. 578-604
    • Sternberg, S.1
  • 58
    • 0000937192 scopus 로고
    • A Model Problem with the Coexistence of Stochastic and Integrable Behavior
    • M. Wojtkowski, "A Model Problem with the Coexistence of Stochastic and Integrable Behavior," Commun. Math. Phys. 80, 453-464 (1981).
    • (1981) Commun. Math. Phys. , vol.80 , pp. 453-464
    • Wojtkowski, M.1
  • 59
    • 0001249689 scopus 로고
    • Melnikov Method and Transversal Homoclinic Points in the Restricted Three-Body Problem
    • Z. Xia, "Melnikov Method and Transversal Homoclinic Points in the Restricted Three-Body Problem," J. Diff. Eqns. 96(1), 170-184 (1992).
    • (1992) J. Diff. Eqns. , vol.96 , Issue.1 , pp. 170-184
    • Xia, Z.1


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