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Volumn 29, Issue 5, 2009, Pages 1479-1513

Non-hyperbolic ergodic measures for non-hyperbolic homoclinic classes

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EID: 74049154692     PISSN: 01433857     EISSN: 14694417     Source Type: Journal    
DOI: 10.1017/S0143385708000849     Document Type: Article
Times cited : (34)

References (57)
  • 4
    • 33847695271 scopus 로고    scopus 로고
    • Pseudo-orbit shadowing in the C1-topology
    • F. Abdenur and L. J. Diáz. Pseudo-orbit shadowing in the C1-topology. Discrete Contin. Dyn. Syst. 17 (2007), 223-245.
    • (2007) Discrete Contin. Dyn. Syst. , vol.17 , pp. 223-245
    • Abdenur, F.1    Diáz, L.J.2
  • 6
    • 0037385190 scopus 로고    scopus 로고
    • On the uniform hyperbolicity of some nonuniformly hyperbolic systems
    • J. Alves, V. Araújo and B. Saussol. On the uniform hyperbolicity of some nonuniformly hyperbolic systems. Proc. Amer. Math. Soc. 131 (2003), 1303-1309.
    • (2003) Proc. Amer. Math. Soc. , vol.131 , pp. 1303-1309
    • Alves, J.1    Araújo, V.2    Saussol, B.3
  • 7
    • 51249168224 scopus 로고
    • The set of Axiom A diffeomorphisms with no cycles
    • N. Aoki. The set of Axiom A diffeomorphisms with no cycles. Bol. Soc. Brasil. Mat. (N.S.) 23 (1992), 21-65.
    • (1992) Bol. Soc. Brasil. Mat. (N.S.) , vol.23 , pp. 21-65
    • Aoki, N.1
  • 9
    • 0036896073 scopus 로고    scopus 로고
    • Genericity of zero Lyapunov exponents
    • J. Bochi. Genericity of zero Lyapunov exponents. Ergod. Th. & Dynam. Sys. 22 (2002), 1667-1696.
    • (2002) Ergod. Th. & Dynam. Sys. , vol.22 , pp. 1667-1696
    • Bochi, J.1
  • 10
    • 0347146025 scopus 로고    scopus 로고
    • Uniform (projective) hyperbolicity or no hyperbolicity: A dichotomy for generic conservative maps
    • J. Bochi and M. Viana. Uniform (projective) hyperbolicity or no hyperbolicity: a dichotomy for generic conservative maps. Ann. Inst. H. Poincaŕe, Anal. Non Lińeaire 19 (2002), 113-123.
    • (2002) Ann. Inst. H. Poincaŕe, Anal. Non Lińeaire , vol.19 , pp. 113-123
    • Bochi, J.1    Viana, M.2
  • 11
    • 4944255089 scopus 로고    scopus 로고
    • Récurrence et généricité
    • Ch. Bonatti and S. Crovisier. Récurrence et géné ricité. Invent. Math. 158 (2004), 33-104.
    • (2004) Invent. Math. , vol.158 , pp. 33-104
    • Bonatti, Ch.1    Crovisier, S.2
  • 12
    • 0039332325 scopus 로고    scopus 로고
    • Nonhyperbolic transitive diffeomorphisms
    • Ch. Bonatti and L. J. Diáz. Nonhyperbolic transitive diffeomorphisms. Ann. of Math. (2) 143 (1996), 357-396.
    • (1996) Ann. of Math. (2) , vol.143 , pp. 357-396
    • Bonatti, Ch.1    Diáz, L.J.2
  • 13
    • 0032622909 scopus 로고    scopus 로고
    • Connexions hétéroclines et genericité d'une infinité de puits ou de sources
    • Ch. Bonatti and L. J. Diáz. Connexions hétéroclines et genericité d'une infinité de puits ou de sources. Ann. Sci. École Norm. Sup. 32 (1999), 135-150.
    • (1999) Ann. Sci. École Norm. Sup. , vol.32 , pp. 135-150
    • Bonatti, Ch.1    Diáz, L.J.2
  • 15
    • 44149109395 scopus 로고    scopus 로고
    • Robust heterodimensional cycles
    • Ch. Bonatti and L. J. Diáz. Robust heterodimensional cycles. J. Inst. Math. Jussieu 7(3) (2008), 469-525.
    • (2008) J. Inst. Math. Jussieu , vol.7 , Issue.3 , pp. 469-525
    • Bonatti, Ch.1    Diáz, L.J.2
  • 16
    • 44249111893 scopus 로고    scopus 로고
    • Super-exponential growth of the number of periodic orbits inside homoclinic classes
    • Ch. Bonatti, L. J. Diáz and T. Fisher. Super-exponential growth of the number of periodic orbits inside homoclinic classes. Discrete Contin. Dyn. Syst. 20 (2008), 589-604.
    • (2008) Discrete Contin. Dyn. Syst. , vol.20 , pp. 589-604
    • Bonatti, Ch.1    Diáz, L.J.2    Fisher, T.3
  • 17
    • 0346829860 scopus 로고    scopus 로고
    • A C1-generic dichotomy for diffeomorphisms: Weak forms of hyperbolicicity or infinitely many sinks or sources
    • Ch. Bonatti, L. J. Diáz and E. R. Pujals. A C1-generic dichotomy for diffeomorphisms: weak forms of hyperbolicicity or infinitely many sinks or sources. Ann. of Math. (2) 158 (2003), 355-418.
    • (2003) Ann. of Math. (2) , vol.158 , pp. 355-418
    • Bonatti, Ch.1    Diáz, L.J.2    Pujals, E.R.3
  • 18
    • 0034165529 scopus 로고    scopus 로고
    • Pas de ' Shadowing Lemma' pour les dynamiques partiellement hyperboliques.
    • Ch. Bonatti, L. J. Diáz and G. Turcat. Pas de 'Shadowing Lemma' pour les dynamiques partiellement hyperboliques. C. R. Acad. Sci., Paris, Śer. I Math. 330(7) (2000), 587-592.
    • (2000) C. R. Acad. Sci., Paris, Śer. i Math. , vol.330 , Issue.7 , pp. 587-592
    • Bonatti, Ch.1    Diáz, L.J.2    Turcat, G.3
  • 21
    • 0034355847 scopus 로고    scopus 로고
    • SRB measures for partially hyperbolic systems whose central direction is mostly contracting
    • Ch. Bonatti and M. Viana. SRB measures for partially hyperbolic systems whose central direction is mostly contracting. Israel J. Math. 115 (2000), 157-193.
    • (2000) Israel J. Math. , vol.115 , pp. 157-193
    • Bonatti, Ch.1    Viana, M.2
  • 23
    • 0242277089 scopus 로고    scopus 로고
    • Non-zero Lyapunov exponents and uniform hyperbolicity
    • DOI 10.1088/0951-7715/16/4/316, PII S0951771503594002
    • Y. Cao. Nonzero Lyapunov exponents and uniformly hyperbolicity. Nonlinearity 16 (2003), 1473-1479. (Pubitemid 37342327)
    • (2003) Nonlinearity , vol.16 , Issue.4 , pp. 1473-1479
    • Cao, Y.1
  • 24
    • 33745228447 scopus 로고    scopus 로고
    • Some non-hyperbolic systems with strictly non-zero Lyapunov exponents for all invariant measures: Horseshoes with internal tangencies
    • Y. Cao, S. Luzzatto and I. Rios. Some non-hyperbolic systems with strictly non-zero Lyapunov exponents for all invariant measures: horseshoes with internal tangencies. Discrete Contin. Dyn. Syst. 15 (2006), 61-71.
    • (2006) Discrete Contin. Dyn. Syst. , vol.15 , pp. 61-71
    • Cao, Y.1    Luzzatto, S.2    Rios, I.3
  • 25
    • 47249159390 scopus 로고    scopus 로고
    • The boundary of hyperbolicity for Henon-like families
    • Y. Cao, S. Luzzatto and I. Rios. The boundary of hyperbolicity for Henon-like families. Ergod. Th. & Dynam. Sys. 28(4) (2008), 1049-1080.
    • (2008) Ergod. Th. & Dynam. Sys. , vol.28 , Issue.4 , pp. 1049-1080
    • Cao, Y.1    Luzzatto, S.2    Rios, I.3
  • 27
    • 84974285024 scopus 로고
    • Robust non-hyperbolic dynamics at heterodimensional cycles
    • L. J. Diáz. Robust non-hyperbolic dynamics at heterodimensional cycles. Ergod. Th. & Dynam. Sys. 15 (1995), 291-315.
    • (1995) Ergod. Th. & Dynam. Sys. , vol.15 , pp. 291-315
    • Diáz, L.J.1
  • 28
    • 0036012122 scopus 로고    scopus 로고
    • Every compact manifold carries a completely hyperbolic diffeomorphism
    • D. Dolgopyat and Ya. Pesin. Every compact manifold carries a completely hyperbolic diffeomorphism. Ergod. Th. & Dynam. Sys. 22 (2002), 409-435.
    • (2002) Ergod. Th. & Dynam. Sys. , vol.22 , pp. 409-435
    • Dolgopyat, D.1    Pesin, Ya.2
  • 29
    • 0040843410 scopus 로고    scopus 로고
    • Partial hyperbolicity and robust transitivity
    • L. J. Diáz, E. R. Pujals and R. Ures. Partial hyperbolicity and robust transitivity. Acta Math. 183 (1999), 1-43.
    • (1999) Acta Math , vol.183 , pp. 1-43
    • Diáz, L.J.1    Pujals, E.R.2    Ures, R.3
  • 30
    • 84966262519 scopus 로고
    • Necessary conditions for stability of diffeomorphisms
    • J. Franks. Necessary conditions for stability of diffeomorphisms. Trans. Amer. Math. Soc. 158 (1971), 301-308.
    • (1971) Trans. Amer. Math. Soc. , vol.158 , pp. 301-308
    • Franks, J.1
  • 31
    • 38349041554 scopus 로고    scopus 로고
    • Regularity of central leaves of partially hyperbolic sets and its applications
    • (Engl. transl. Izv. Math. 70(6) (2006), 1093-1116)
    • A. Gorodetski. Regularity of central leaves of partially hyperbolic sets and its applications. Izv. Ross. Akad. Nauk Ser. Mat. 70(6) (2006), 19-44 (Engl. transl. Izv. Math. 70(6) (2006), 1093-1116).
    • (2006) Izv. Ross. Akad. Nauk Ser. Mat. , vol.70 , Issue.6 , pp. 19-44
    • Gorodetski, A.1
  • 32
    • 27544511576 scopus 로고    scopus 로고
    • Some new robust properties of invariant sets and attractors of dynamical systems
    • A. Gorodetski and Yu. Ilyashenko. Some new robust properties of invariant sets and attractors of dynamical systems. Funct. Anal. Appl. 33 (1999), 16-30.
    • (1999) Funct. Anal. Appl. , vol.33 , pp. 16-30
    • Gorodetski, A.1    Ilyashenko, Yu.2
  • 33
    • 32044440361 scopus 로고    scopus 로고
    • Some properties of skew products over the horseshoe and solenoid
    • A. Gorodetski and Yu. Ilyashenko. Some properties of skew products over the horseshoe and solenoid. Proc. Steklov Inst. 231 (2000), 96-118.
    • (2000) Proc. Steklov Inst. , vol.231 , pp. 96-118
    • Gorodetski, A.1    Ilyashenko, Yu.2
  • 36
    • 43949172086 scopus 로고
    • On models with nonrough Poincaré homoclinic curves (Homoclinic chaos (Brussels, 1991))
    • S. V. Gonchenko, L. P. Shilnikov and D. V. Turaev. On models with nonrough Poincaré homoclinic curves (Homoclinic chaos (Brussels, 1991)). Phys. D 62 (1993), 1-14.
    • (1993) Phys. D , vol.62 , pp. 1-14
    • Gonchenko, S.V.1    Shilnikov, L.P.2    Turaev, D.V.3
  • 37
    • 0031480448 scopus 로고    scopus 로고
    • 1-stability and ω-stability conjectures for flows
    • 1-stability and ω-stability conjectures for flows. Ann. of Math. (2) 145 (1997), 81-137.
    • (1997) Ann. of Math. (2) , vol.145 , pp. 81-137
    • Hayashi, S.1
  • 38
    • 0034349439 scopus 로고    scopus 로고
    • Generic diffeomorphisms with superexponential growth of number of periodic points
    • V. Kaloshin. Generic diffeomorphisms with superexponential growth of number of periodic points. Comm. Math. Phys. 211 (2000), 253-271.
    • (2000) Comm. Math. Phys. , vol.211 , pp. 253-271
    • Kaloshin, V.1
  • 40
    • 0010885480 scopus 로고
    • Approximation of ergodic dynamical systems by periodic transformations
    • A. Katok and A. Stepin. Approximation of ergodic dynamical systems by periodic transformations. Dokl. Akad. Nauk. SSSR 171 (1966), 1268-1271.
    • (1966) Dokl. Akad. Nauk. SSSR , vol.171 , pp. 1268-1271
    • Katok, A.1    Stepin, A.2
  • 41
    • 0001834320 scopus 로고
    • Approximations in ergodic theory
    • A. Katok and A. Stepin. Approximations in ergodic theory. Russian Math. Surveys 22 (1967), 81-106.
    • (1967) Russian Math. Surveys , vol.22 , pp. 81-106
    • Katok, A.1    Stepin, A.2
  • 43
    • 0000201494 scopus 로고
    • An ergodic closing lemma
    • R. Mañé. An ergodic closing lemma. Ann. of Math. (2) 116 (1982), 503-540.
    • (1982) Ann. of Math. (2) , vol.116 , pp. 503-540
    • Mañé, R.1
  • 47
    • 84966239850 scopus 로고
    • Hyperbolic limit sets
    • S. Newhouse. Hyperbolic Limit Sets. Trans. Amer. Math. Soc. 167 (1972), 125-150.
    • (1972) Trans. Amer. Math. Soc. , vol.167 , pp. 125-150
    • Newhouse, S.1
  • 48
    • 51249181043 scopus 로고
    • The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms
    • S. Newhouse. The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms. Publ. Math. Inst. Hautes Études Sci. 50 (1979), 101-151.
    • (1979) Publ. Math. Inst. Hautes Études Sci. , vol.50 , pp. 101-151
    • Newhouse, S.1
  • 49
    • 0038434713 scopus 로고
    • A multiplicative ergodic theorem. Characteristic Lyapunov exponents of dynamical systems
    • (in Russian)
    • V. I. Oseledec. A multiplicative ergodic theorem. Characteristic Lyapunov exponents of dynamical systems. Trudy Moskov. Mat. Ob. 19 (1968), 179-210 (in Russian).
    • (1968) Trudy Moskov. Mat. Ob. , vol.19 , pp. 179-210
    • Oseledec, V.I.1
  • 50
    • 33749569489 scopus 로고    scopus 로고
    • A global view of dynamics and a conjecture on the denseness of finitude of attractors (Géométrie complexe et systémes dynamiques (Orsay, 1995))
    • J. Palis. A global view of dynamics and a conjecture on the denseness of finitude of attractors (Géométrie complexe et systémes dynamiques (Orsay, 1995)). Asterisque 261 (2000), 335-347.
    • (2000) Asterisque , vol.261 , pp. 335-347
    • Palis, J.1
  • 51
    • 84961291543 scopus 로고
    • Characteristic Lyapunov exponents and smooth ergodic theory
    • Ya. Pesin. Characteristic Lyapunov exponents and smooth ergodic theory. Usp. Mat. Nauk 32 (1977), 55-112.
    • (1977) Usp. Mat. Nauk , vol.32 , pp. 55-112
    • Pesin, Ya.1
  • 52
    • 0034347511 scopus 로고    scopus 로고
    • Homoclinic tangencies and hyperbolicity for surface diffeomorphisms
    • E. R. Pujals and M. Sambarino. Homoclinic tangencies and hyperbolicity for surface diffeomorphisms. Ann. of Math. (2) 151 (2000), 961-1023.
    • (2000) Ann. of Math. (2) , vol.151 , pp. 961-1023
    • Pujals, E.R.1    Sambarino, M.2
  • 53
    • 44249110058 scopus 로고    scopus 로고
    • 1-stable shadowing chain components
    • 1-stable shadowing chain components. Ergod. Th. & Dynam. Sys. 28(3) (2008), 987-1029.
    • (2008) Ergod. Th. & Dynam. Sys. , vol.28 , Issue.3 , pp. 987-1029
    • Sakai, K.1
  • 54
    • 0034348989 scopus 로고    scopus 로고
    • Pathological foliations and removable zero exponents
    • M. Shub and A. Wilkinson. Pathological foliations and removable zero exponents. Invent. Math. 139 (2000), 495-508.
    • (2000) Invent. Math. , vol.139 , pp. 495-508
    • Shub, M.1    Wilkinson, A.2
  • 55
    • 0007348981 scopus 로고
    • Heteroclinic attractors: Time averages and moduli of topological conjugacy
    • F. Takens. Heteroclinic attractors: time averages and moduli of topological conjugacy. Bol. Soc. Brasil. Mat. (N.S.) 25 (1994), 107-120.
    • (1994) Bol. Soc. Brasil. Mat. (N.S.) , vol.25 , pp. 107-120
    • Takens, F.1
  • 57
    • 22844453875 scopus 로고    scopus 로고
    • An open set of maps for which every point is absolutely nonshadowable
    • G.-C. Yuan and J. A. Yorke. An open set of maps for which every point is absolutely nonshadowable. Proc. Amer. Math. Soc. 128 (2000), 909-918.
    • (2000) Proc. Amer. Math. Soc. , vol.128 , pp. 909-918
    • Yuan, G.-C.1    Yorke, J.A.2


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