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Volumn 126, Issue 4, 2005, Pages 1317-1343

On dynamic properties of diffeomorphisms with homoclinic tangency

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EID: 17644427641     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (16)

References (33)
  • 1
    • 0000936975 scopus 로고
    • On three-dimensional systems close to a system with a nonrough homoclinic curve, I, II
    • N. K. Gavrilov and L. P. Shil'nikov, "On three-dimensional systems close to a system with a nonrough homoclinic curve, I, II," Mat. Sb., 88, No. 4, 475-492 (1972); 90, No. 1, 139-157 (1973).
    • (1972) Mat. Sb. , vol.88 , Issue.4 , pp. 475-492
    • Gavrilov, N.K.1    Shil'nikov, L.P.2
  • 2
    • 0000936968 scopus 로고
    • N. K. Gavrilov and L. P. Shil'nikov, "On three-dimensional systems close to a system with a nonrough homoclinic curve, I, II," Mat. Sb., 88, No. 4, 475-492 (1972); 90, No. 1, 139-157 (1973).
    • (1973) Mat. Sb. , vol.90 , Issue.1 , pp. 139-157
  • 3
    • 0041801952 scopus 로고
    • On stable periodic motions of systems close to systems with a nonrough homoclinic curve
    • S. V. Gonchenko, "On stable periodic motions of systems close to systems with a nonrough homoclinic curve," Mat. Zametki, 33, No. 5, 745-755 (1983).
    • (1983) Mat. Zametki , vol.33 , Issue.5 , pp. 745-755
    • Gonchenko, S.V.1
  • 5
    • 17644417180 scopus 로고    scopus 로고
    • Dynamics and moduli of Ω-conjugacy of 4D-diffeomorphisms with a structurally unstable homoclinic orbit to a saddle-focus fixed point
    • S. V. Gonchenko, "Dynamics and moduli of Ω-conjugacy of 4D-diffeomorphisms with a structurally unstable homoclinic orbit to a saddle-focus fixed point," Amer. Trans. Math., 200, No. 2, 107-134 (2000).
    • (2000) Amer. Trans. Math. , vol.200 , Issue.2 , pp. 107-134
    • Gonchenko, S.V.1
  • 6
    • 17644424032 scopus 로고    scopus 로고
    • Homoclinic tangencies, Ω-moduli, and bifurcations
    • S. V. Gonchenko, "Homoclinic tangencies, Ω-moduli, and bifurcations," Tr. Mat. Inst. Steklova, 236 (2002).
    • (2002) Tr. Mat. Inst. Steklova , vol.236
    • Gonchenko, S.V.1
  • 8
    • 17644389275 scopus 로고    scopus 로고
    • On Hopf bifurcations of closed invariant curves in the case of two-dimensional diffeomorphisms with a homoclinic tangency
    • (in press).
    • S. V. Gonchenko and V. S. Gonchenko, "On Hopf bifurcations of closed invariant curves in the case of two-dimensional diffeomorphisms with a homoclinic tangency," Tr. Mat. Inst. Steklova (in press).
    • Tr. Mat. Inst. Steklova
    • Gonchenko, S.V.1    Gonchenko, V.S.2
  • 9
    • 0011541555 scopus 로고
    • Ω-Conjugacy invariants of diffeomorphisms with a nonrough homoclinic trajectory
    • S. V. Gonchenko and L. P. Shil'nikov, "Ω-Conjugacy invariants of diffeomorphisms with a nonrough homoclinic trajectory," Ukr. Mat. Zh., 42, No. 2, 153-159 (1990).
    • (1990) Ukr. Mat. Zh. , vol.42 , Issue.2 , pp. 153-159
    • Gonchenko, S.V.1    Shil'nikov, L.P.2
  • 10
    • 0001096995 scopus 로고
    • On moduli of systems with a nonrough Poincaré homoclinic curve
    • S. V. Gonchenko and L. P. Shil'nikov, "On moduli of systems with a nonrough Poincaré homoclinic curve," Izv. Ross. Akad. Nauk, Ser. Mat., 56, No. 6, 1165-1196 (1992).
    • (1992) Izv. Ross. Akad. Nauk, Ser. Mat. , vol.56 , Issue.6 , pp. 1165-1196
    • Gonchenko, S.V.1    Shil'nikov, L.P.2
  • 11
    • 0011667119 scopus 로고
    • On dynamic systems with nonrough homoclinic curves
    • S. V. Gonchenko and L. P. Shil'nikov, "On dynamic systems with nonrough homoclinic curves," Dokl. Akad. Nauk SSSR, 286, No. 5, 1049-105 (1986).
    • (1986) Dokl. Akad. Nauk SSSR , vol.286 , Issue.5 , pp. 1049-1105
    • Gonchenko, S.V.1    Shil'nikov, L.P.2
  • 12
    • 0002223695 scopus 로고
    • On arithmetical properties of topological invariants of systems with a nonrough homoclinic trajectory
    • S. V. Gonchenko and L. P. Shil'nikov, "On arithmetical properties of topological invariants of systems with a nonrough homoclinic trajectory," Ukr. Mat. Zh., 39, No. 1, 21-28 (1987).
    • (1987) Ukr. Mat. Zh. , vol.39 , Issue.1 , pp. 21-28
    • Gonchenko, S.V.1    Shil'nikov, L.P.2
  • 14
    • 43949172086 scopus 로고    scopus 로고
    • On models with nonrough Poincaré homoclinic curves
    • S. V. Gonchenko, L. P. Shil'nikov, and D. V. Turaev, "On models with nonrough Poincaré homoclinic curves," Physica D, 62, Nos. 1-4,1-14
    • Physica D , vol.62 , Issue.1-4 , pp. 1-14
    • Gonchenko, S.V.1    Shil'nikov, L.P.2    Turaev, D.V.3
  • 15
    • 0005283382 scopus 로고    scopus 로고
    • Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits
    • S. V. Gonchenko, L. P. Shil'nikov, and D. V. Turaev, "Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits," Interdiscip. J. Chaos, 6, No. 1, 15-31 (1996).
    • (1996) Interdiscip. J. Chaos , vol.6 , Issue.1 , pp. 15-31
    • Gonchenko, S.V.1    Shil'nikov, L.P.2    Turaev, D.V.3
  • 16
    • 0001684820 scopus 로고
    • On models with nonrough Poincaré homoclinic curves
    • S. V. Gonchenko, D. V. Turaev, and L. P. Shil'nikov, "On models with nonrough Poincaré homoclinic curves," Dokl. Akad. Nauk SSSR, 320, No. 2, 269-272 (1991).
    • (1991) Dokl. Akad. Nauk SSSR , vol.320 , Issue.2 , pp. 269-272
    • Gonchenko, S.V.1    Turaev, D.V.2    Shil'nikov, L.P.3
  • 17
    • 0010196406 scopus 로고
    • On the existence of Newhouse domains near systems with a nonrough homoclinic curve (higher-dimensional case)
    • S. V. Gonchenko, D. V. Turaev, and L. P. Shil'nikov, "On the existence of Newhouse domains near systems with a nonrough homoclinic curve (higher-dimensional case)," Dokl. Ross. Akad. Nauk, 329, No. 4, 404-407 (1993).
    • (1993) Dokl. Ross. Akad. Nauk , vol.329 , Issue.4 , pp. 404-407
    • Gonchenko, S.V.1    Turaev, D.V.2    Shil'nikov, L.P.3
  • 18
    • 0010143093 scopus 로고
    • Dynamical phenomena in higher-dimensional systems with a nonrough Poincaré homoclinic curve
    • S. V. Gonchenko, D. V. Turaev, and L. P. Shil'nikov, "Dynamical phenomena in higher-dimensional systems with a nonrough Poincaré homoclinic curve," Dokl. Ross. Akad. Nauk, 330, No. 2, 144-147 (1993).
    • (1993) Dokl. Ross. Akad. Nauk , vol.330 , Issue.2 , pp. 144-147
    • Gonchenko, S.V.1    Turaev, D.V.2    Shil'nikov, L.P.3
  • 19
    • 0002058632 scopus 로고    scopus 로고
    • On the Newhouse domains of two-dimensional diffeomorphisms close to a diffeomorphism with a nonrough heteroclinic contour
    • S. V. Gonchenko, D. V. Turaev, and L. P. Shil'nikov, "On the Newhouse domains of two-dimensional diffeomorphisms close to a diffeomorphism with a nonrough heteroclinic contour," Tr. Mat. Inst. Steklova, 216, 7-118 (1997).
    • (1997) Tr. Mat. Inst. Steklova , vol.216 , pp. 7-118
    • Gonchenko, S.V.1    Turaev, D.V.2    Shil'nikov, L.P.3
  • 21
    • 32044475236 scopus 로고
    • Diffeomorphisms with infinitely many sinks
    • S. Newhouse, "Diffeomorphisms with infinitely many sinks," Topology, 13, 9-18 (1974).
    • (1974) Topology , vol.13 , pp. 9-18
    • Newhouse, S.1
  • 22
    • 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. IHES, 50, 101-151 (1979).
    • (1979) Publ. Math. IHES , vol.50 , pp. 101-151
    • Newhouse, S.E.1
  • 23
    • 0000109928 scopus 로고
    • Systems with a homoclinic curve of a higher-dimensional saddle-focus and the spiral chaos
    • I. M. Ovsyannikov and L. P. Shil'nikov, "Systems with a homoclinic curve of a higher-dimensional saddle-focus and the spiral chaos," Mat. Sb., 182, 1043-1073 (1991).
    • (1991) Mat. Sb. , vol.182 , pp. 1043-1073
    • Ovsyannikov, I.M.1    Shil'nikov, L.P.2
  • 24
    • 0039023464 scopus 로고
    • High dimension diffeomorphisms displaying infinitely many sinks
    • J. Palis and M. Viana, "High dimension diffeomorphisms displaying infinitely many sinks," Ann. Math., 140, 91-136 (1994).
    • (1994) Ann. Math. , vol.140 , pp. 91-136
    • Palis, J.1    Viana, M.2
  • 25
    • 84974408747 scopus 로고
    • Persistence of homoclinic tangencies in higher dimensions
    • N. Romero, "Persistence of homoclinic tangencies in higher dimensions," Ergod. Theory Dyn. Syst., 15, 735-757 (1995).
    • (1995) Ergod. Theory Dyn. Syst. , vol.15 , pp. 735-757
    • Romero, N.1
  • 27
    • 0000063614 scopus 로고
    • On a Poincaré-Birkhoff problem
    • L. P. Shil'nikov, "On a Poincaré-Birkhoff problem," Mat. Sb., 74, No. 4, 378-397 (1967).
    • (1967) Mat. Sb. , vol.74 , Issue.4 , pp. 378-397
    • Shil'nikov, L.P.1
  • 29
    • 0002737270 scopus 로고
    • Diffeomorphisms with many periodic points
    • Princeton Univ. Press
    • S. Smale, "Diffeomorphisms with many periodic points," in: Differential and Combinatorial Topology, Princeton Univ. Press (1965), pp. 63-80.
    • (1965) Differential and Combinatorial Topology , pp. 63-80
    • Smale, S.1
  • 30
    • 0042302939 scopus 로고    scopus 로고
    • On bifurcations of periodic trajectories in a neighborhood of a nonrough homoclinic curve
    • O. V. Sten'kin and L. P. Shil'nikov, "On bifurcations of periodic trajectories in a neighborhood of a nonrough homoclinic curve," Differents. Uravn., 33, No. 3, 377-384 (1997).
    • (1997) Differents. Uravn. , vol.33 , Issue.3 , pp. 377-384
    • Sten'kin, O.V.1    Shil'nikov, L.P.2
  • 31
    • 0035628941 scopus 로고    scopus 로고
    • Three-dimensional dissipative diffeomorphisms with homoclinic tangencies
    • J. C. Tatjer, "Three-dimensional dissipative diffeomorphisms with homoclinic tangencies," Ergod. Theory Dyn. Syst., 21, 249-302 (2001).
    • (2001) Ergod. Theory Dyn. Syst. , vol.21 , pp. 249-302
    • Tatjer, J.C.1
  • 32
    • 17644415794 scopus 로고    scopus 로고
    • Example of a wild strange attractor
    • D. V. Turaev and L. P. Shil'nikov, "Example of a wild strange attractor," Mat. Sb., 189, No. 2, 137-160 (1998).
    • (1998) Mat. Sb. , vol.189 , Issue.2 , pp. 137-160
    • Turaev, D.V.1    Shil'nikov, L.P.2
  • 33
    • 0030136340 scopus 로고    scopus 로고
    • On the dimension of nonlocal bifurcation problems
    • D. V. Turaev, "On the dimension of nonlocal bifurcation problems," Int. J. Bifurcation Chaos, 6, No. 5, 919-948 (1996).
    • (1996) Int. J. Bifurcation Chaos , vol.6 , Issue.5 , pp. 919-948
    • Turaev, D.V.1


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