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Volumn 364, Issue 10, 2012, Pages 5111-5148

Abundance of c 1-robust homoclinic tangencies

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EID: 84862835792     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-2012-05445-6     Document Type: Article
Times cited : (68)

References (33)
  • 1
    • 32544443472 scopus 로고    scopus 로고
    • Generic diffeomorphisms on compact surfaces
    • Mr2214876 (2006m:37024)
    • F. Abdenur, Ch. Bonatti, S. Crovisier, L. J. Díaz, Generic diffeomorphisms on compact surfaces, Fund. Math. 187 (2005), 127-159. Mr2214876 (2006m:37024)
    • (2005) Fund. Math , vol.187 , pp. 127-159
    • Abdenur, F.1    Bonatti, C.2    Crovisier, S.3    Díaz, L.J.4
  • 3
    • 0001874180 scopus 로고
    • Nongenericity of Ω-stability in Global Analysis
    • Amer. Math. Soc., Providence, R.I., Mr0271986 (42:6867)
    • R. Abraham, S. Smale, Nongenericity of Ω-stability in Global Analysis, Proc. Sympos. Pure Math., Vol. XIV, 5-8 (Amer. Math. Soc., Providence, R.I., 1968). Mr0271986 (42:6867)
    • (1968) Proc. Sympos. Pure Math , vol.14 , pp. 5-8
    • Abraham, R.1    Smale, S.2
  • 4
    • 67349115475 scopus 로고    scopus 로고
    • 1-persistent homoclinic tangency for higher dimensions
    • Mr2358509 (2008k:37049)
    • 1-persistent homoclinic tangency for higher dimensions, Proc. Amer. Math. Soc. 136 (2008), 677-686. Mr2358509 (2008k:37049)
    • (2008) Proc. Amer. Math. Soc , vol.136 , pp. 677-686
    • Asaoka, M.1
  • 5
    • 0001870459 scopus 로고
    • The dynamics of the Hénon map
    • Mr1087346 (92d:58116)
    • M. Benedicks, L. Carleson, The dynamics of the Hénon map, Ann. of Math. 133 (1991), 73-169. Mr1087346 (92d:58116)
    • (1991) Ann. of Math , vol.133 , pp. 73-169
    • Benedicks, M.1    Carleson, L.2
  • 7
    • 4944255089 scopus 로고    scopus 로고
    • Récurrence et généricité
    • Mr2090361 (2007b:37036)
    • Ch. Bonatti, S. Crovisier, Récurrence et généricité, Inventiones Math. 158 (2004), 33-104. Mr2090361 (2007b:37036)
    • (2004) Inventiones Math , vol.158 , pp. 33-104
    • Bonatti, C.1    Crovisier, S.2
  • 8
    • 0039332325 scopus 로고    scopus 로고
    • Nonhyperbolic transitive diffeomorphisms
    • Mr1381990 (97d:58122)
    • Ch. Bonatti, L. J. Díaz, Nonhyperbolic transitive diffeomorphisms, Ann. of Math. 143 (1996) 357-396. Mr1381990 (97d:58122)
    • (1996) Ann. of Math , vol.143 , pp. 357-396
    • Bonatti, C.1    Díaz, L.J.2
  • 10
    • 0346829860 scopus 로고    scopus 로고
    • 1-generic dichotomy for diffeomorphisms: Weak forms of hyperbolicity or infinitely many sinks or sources
    • Mr2018925 (2007k:37032)
    • 1-generic dichotomy for diffeomorphisms: Weak forms of hyperbolicity or infinitely many sinks or sources, Ann. of Math. 158 (2003), 355-418. Mr2018925 (2007k:37032)
    • (2003) Ann. of Math , vol.158 , pp. 355-418
    • Bonatti, C.1    Díaz, L.J.2    Pujals, E.R.3
  • 11
    • 18844461740 scopus 로고    scopus 로고
    • Robustly transitive sets and heterodimensional cycles
    • Mr2052302 (2005d:37038)
    • Bonatti, L. J. Díaz, E. R. Pujals, J. Rocha, Robustly transitive sets and heterodimensional cycles, Astérisque 286 (2003) 187-222. Mr2052302 (2005d:37038)
    • (2003) Astérisque , vol.286 , pp. 187-222
  • 12
    • 0007393133 scopus 로고
    • Discontinuity of the Hausdorff dimension of hyperbolic sets
    • Mr1323944 (95m:58085)
    • Ch. Bonatti, L. J. Díaz, M. Viana, Discontinuity of the Hausdorff dimension of hyperbolic sets, C. R. Acad. Sci. Paris Sér. I Math. 320 (1995), 713-718. Mr1323944 (95m:58085)
    • (1995) C. R. Acad. Sci. Paris Sér. I Math , vol.320 , pp. 713-718
    • Bonatti, C.1    Díaz, L.J.2    Viana, M.3
  • 13
    • 33746377160 scopus 로고    scopus 로고
    • Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective
    • (Mathematical Physics), Springer-Verlag, Mr2105774 (2005g:37001)
    • Ch. Bonatti, L. J. Díaz, M. Viana, Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective, in Encyclopaedia of Mathematical Sciences (Mathematical Physics), 102 Springer-Verlag, 2005. Mr2105774 (2005g:37001)
    • (2005) Encyclopaedia of Mathematical Sciences , vol.102
    • Bonatti, C.1    Díaz, J.2    Viana, M.3
  • 14
    • 0034355847 scopus 로고    scopus 로고
    • SRB measures for partially hyperbolic systems whose central direction is mostly contracting
    • Mr1749677 (2001j:37063a)
    • Ch. Bonatti, M. Viana, SRB measures for partially hyperbolic systems whose central direction is mostly contracting, Israel J. Math. 115 (2000), 157-193. Mr1749677 (2001j:37063a)
    • (2000) Israel J. Math , vol.115 , pp. 157-193
    • Bonatti, C.1    Viana, M.2
  • 15
    • 18244372671 scopus 로고    scopus 로고
    • Symbolic extensions and smooth dynamical systems
    • Mr2178700 (2006j:37021)
    • T. Downarowicz, S. Newhouse, Symbolic extensions and smooth dynamical systems, Invent. Math. 160 (2005), 453-499. Mr2178700 (2006j:37021)
    • (2005) Invent. Math , vol.160 , pp. 453-499
    • Downarowicz, T.1    Newhouse, S.2
  • 17
    • 79958795117 scopus 로고    scopus 로고
    • 1-stable intersections of regular Cantor sets
    • 1-stable intersections of regular Cantor sets, Acta Mathematica 206 (2011), 311-323.
    • (2011) Acta Mathematica , vol.206 , pp. 311-323
    • Moreira, C.G.1
  • 18
    • 0031480448 scopus 로고    scopus 로고
    • 1-stability and Ω-stability conjectures for flows
    • Mr1432037 (98b:58096)
    • 1-stability and Ω- stability conjectures for flows, Ann. of Math. 145 (1997), 81-137. Mr1432037 (98b:58096)
    • (1997) Ann. of Math , vol.145 , pp. 81-137
    • Hayashi, S.1
  • 19
    • 0033235416 scopus 로고    scopus 로고
    • An extension of the Artin-Mazur theorem
    • Mr1726706 (2000j:37020)
    • V. Y. Kaloshin, An extension of the Artin-Mazur theorem, Ann. of Math. 150 (1999), 729-741. Mr1726706 (2000j:37020)
    • (1999) Ann. of Math , vol.150 , pp. 729-741
    • Kaloshin, V.Y.1
  • 20
    • 0242344635 scopus 로고
    • Abundance of strange attractors
    • Mr1237897 (94k:58089)
    • L. Mora, M. Viana, Abundance of strange attractors, Acta Math. 171 (1993), 1-71. Mr1237897 (94k:58089)
    • (1993) Acta Math , vol.171 , pp. 1-71
    • Mora, L.1    Viana, M.2
  • 21
    • 0000935850 scopus 로고
    • 2
    • Proc. Sympos. Pure Math., Vol., Berkeley, Calif., 1968, Amer. Math. Soc., Providence, R.I. Mr0277005 (43:2742)
    • 2, Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968) (1970) 191-202, Amer. Math. Soc., Providence, R.I. Mr0277005 (43:2742)
    • (1970) Global Analysis , vol.14 , pp. 191-202
    • Newhouse, S.1
  • 22
    • 51249181043 scopus 로고
    • The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms
    • MR556584 (82e:58067)
    • S. Newhouse, The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms, Inst. Hautes Études Sci. Publ. Math. 50 (1979), 101-151 MR556584 (82e:58067)
    • (1979) Inst. Hautes Études Sci. Publ. Math , vol.50 , pp. 101-151
    • Newhouse, S.1
  • 23
    • 33749569489 scopus 로고    scopus 로고
    • A global view of dynamics and a conjecture on the denseness of finitude of attractors
    • Mr1755446 (2001d:37025)
    • J. Palis, A global view of dynamics and a conjecture on the denseness of finitude of attractors, Astrísque 261 (2000), 335-347. Mr1755446 (2001d:37025)
    • (2000) Astrísque , vol.261 , pp. 335-347
    • Palis, J.1
  • 24
    • 0003267742 scopus 로고
    • Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations
    • Mr1237641 (94h:58129)
    • J. Palis and F. Takens, Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge Studies in Advanced Mathematics, 35 (1993). Mr1237641 (94h:58129)
    • (1993) Cambridge Studies In Advanced Mathematics , pp. 35
    • Palis, J.1    Takens, F.2
  • 25
    • 0000298739 scopus 로고
    • High dimension diffeomorphisms displaying infinitely many periodic attractors
    • Mr1289496 (95g:58140
    • J. Palis, M. Viana, High dimension diffeomorphisms displaying infinitely many periodic attractors, Ann. of Math. 140 (1994), 207-250. Mr1289496 (95g:58140)
    • (1994) Ann. of Math , vol.140 , pp. 207-250
    • Palis, J.1    Viana, M.2
  • 26
    • 0034347511 scopus 로고    scopus 로고
    • Homoclinic tangencies and hyperbolicity for surface diffeomorphisms
    • Mr1779562 (2001m:37057)
    • E. Pujals, M. Sambarino, Homoclinic tangencies and hyperbolicity for surface diffeomorphisms, Ann. Math. 151 (2000), 961-1023. Mr1779562 (2001m:37057)
    • (2000) Ann. Math , vol.151 , pp. 961-1023
    • Pujals, E.1    Sambarino, M.2
  • 27
    • 84974408747 scopus 로고
    • Persistence of homoclinic tangencies in higher dimensions
    • Mr1346398 (96e:58118)
    • N. Romero, Persistence of homoclinic tangencies in higher dimensions, Ergodic Theory Dynam. Systems 15 (1995), 735-757. Mr1346398 (96e:58118)
    • (1995) Ergodic Theory Dynam. Systems , vol.15 , pp. 735-757
    • Romero, N.1
  • 28
    • 0003178980 scopus 로고
    • 3) and the nongenericity of rational zeta function
    • Mr0317356 (47:5903)
    • 3) and the nongenericity of rational zeta function, Trans. A.M.S. 174 (1972), 217-242. Mr0317356 (47:5903)
    • (1972) Trans. A.M.S , vol.174 , pp. 217-242
    • Simon, C.P.1
  • 29
    • 84968514104 scopus 로고
    • Differentiable dynamical systems
    • Mr0228014 (37:3598)
    • S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc., 73 (1967), 747-817. Mr0228014 (37:3598)
    • (1967) Bull. Amer. Math. Soc , vol.73 , pp. 747-817
    • Smale, S.1
  • 30
    • 0009132956 scopus 로고
    • 1 topology
    • Mr1355140 (96i:58135)
    • 1 topology, Ann. Sci. École Norm. Sup. 28 (1995), 747-760. Mr1355140 (96i:58135)
    • (1995) Ann. Sci. École Norm. Sup , vol.28 , pp. 747-760
    • Ures, R.1
  • 31
    • 12444320405 scopus 로고    scopus 로고
    • Generic diffeomorphisms away from homoclinic tangencies and heterodimensional cycles
    • Mr2106314 (2005i:37035)
    • L. Wen, Generic diffeomorphisms away from homoclinic tangencies and heterodimensional cycles, Bull. Braz. Math. Soc. (N.S.) 35 (2004), 419-452. Mr2106314 (2005i:37035)
    • (2004) Bull. Braz. Math. Soc.(N.S.) , vol.35 , pp. 419-452
    • Wen, L.1
  • 32
    • 0041972666 scopus 로고    scopus 로고
    • Homoclinic tangencies and dominated splittings
    • Mr1925423 (2003f:37055)
    • L. Wen, Homoclinic tangencies and dominated splittings, Nonlinearity 15 (2002), 1445-1469. Mr1925423 (2003f:37055)
    • (2002) Nonlinearity , vol.15 , pp. 1445-1469
    • Wen, L.1


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