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Volumn 132, Issue 3, 1998, Pages 633-680

Non-uniform hyperbolicity and universal bounds for S-unimodal maps

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EID: 0032382986     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220050236     Document Type: Article
Times cited : (65)

References (38)
  • 1
    • 0000640307 scopus 로고    scopus 로고
    • Strong stochastic stability and rate of mixing for unimodal maps
    • V. Baladi, M. Viana: Strong stochastic stability and rate of mixing for unimodal maps. Ann. Sci. École Norm. Sup., 29(4), 483-517 (1996)
    • (1996) Ann. Sci. École Norm. Sup. , vol.29 , Issue.4 , pp. 483-517
    • Baladi, V.1    Viana, M.2
  • 2
    • 0001870459 scopus 로고
    • The dynamics of the Hénon map
    • M. Benedicks, L. Carleson: The dynamics of the Hénon map. Ann. of Math., 133, 73-169 (1991)
    • (1991) Ann. of Math. , vol.133 , pp. 73-169
    • Benedicks, M.1    Carleson, L.2
  • 3
    • 0011613307 scopus 로고
    • Measure of soleniodal attractors of unimodal maps of the segment
    • Nov
    • A. Blokh: M.Y. Lyubich: Measure of soleniodal attractors of unimodal maps of the segment. Math. Notes, 48(5), 1085-1090, Nov 1990
    • (1990) Math. Notes , vol.48 , Issue.5 , pp. 1085-1090
    • Blokh, A.1    Lyubich, M.Y.2
  • 6
    • 0002525106 scopus 로고
    • Positive Liapunov exponents and absolute continuity for maps of the interval
    • P. Collet, J.-P. Eckmann: Positive Liapunov exponents and absolute continuity for maps of the interval. Ergodic Theory Dynamical Systems, 3, 13-46 (1983)
    • (1983) Ergodic Theory Dynamical Systems , vol.3 , pp. 13-46
    • Collet, P.1    Eckmann, J.-P.2
  • 10
    • 0039145291 scopus 로고    scopus 로고
    • Generic hyperbolicity in the logistic family
    • To appear
    • J. Graczyk, G. Świa̧tek. Generic hyperbolicity in the logistic family. To appear in Ann. of Math
    • Ann. of Math
    • Graczyk, J.1    Świa̧tek, G.2
  • 11
    • 0009077570 scopus 로고
    • Sensitive dependence to initial conditions for one dimensional maps
    • J. Guckenheimer: Sensitive dependence to initial conditions for one dimensional maps. Comm. Math. Phys., 70, 133-160 (1979)
    • (1979) Comm. Math. Phys. , vol.70 , pp. 133-160
    • Guckenheimer, J.1
  • 13
    • 0000868141 scopus 로고
    • The topological entropy of the transformation x→ax(1 - x)
    • F. Hofbauer: The topological entropy of the transformation x→ax(1 - x). Monatsh. Math., 90, 117-141 (1980)
    • (1980) Monatsh. Math. , vol.90 , pp. 117-141
    • Hofbauer, F.1
  • 14
    • 0001142190 scopus 로고
    • Quadratic maps without asymptotic measure
    • F. Hofbauer, G. Keller: Quadratic maps without asymptotic measure. Comm. Math. Phys., 127(2), 319-337 (1990)
    • (1990) Comm. Math. Phys. , vol.127 , Issue.2 , pp. 319-337
    • Hofbauer, F.1    Keller, G.2
  • 15
    • 0002053804 scopus 로고
    • Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
    • M. Jakobson: Absolutely continuous invariant measures for one-parameter families of one-dimensional maps. Comm. Math. Phys., 81(1), 39-88 (1981)
    • (1981) Comm. Math. Phys. , vol.81 , Issue.1 , pp. 39-88
    • Jakobson, M.1
  • 16
    • 84975966117 scopus 로고
    • Metric properties of non-renormalizable S-unimodal maps II. Quasi-symmetric conjugacy classes
    • M. Jakobson, G. Świa̧tek: Metric properties of non-renormalizable S-unimodal maps II. Quasi-symmetric conjugacy classes. Ergodic Theory Dynamical Systems, 15(5), 871-938 (1995)
    • (1995) Ergodic Theory Dynamical Systems , vol.15 , Issue.5 , pp. 871-938
    • Jakobson, M.1    Świa̧tek, G.2
  • 17
    • 0002160620 scopus 로고
    • Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps
    • G. Keller, T. Nowicki: Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps. Comm. Math. Phys., 149(1), 31-69 (1992)
    • (1992) Comm. Math. Phys. , vol.149 , Issue.1 , pp. 31-69
    • Keller, G.1    Nowicki, T.2
  • 19
    • 0039737648 scopus 로고    scopus 로고
    • Local connectivity of the Julia set of real polynomials
    • SUNY Stony Brook preprint ims95-5. To appear
    • G. Levin. S. van Strien: Local connectivity of the Julia set of real polynomials. SUNY Stony Brook preprint ims95-5. To appear in Ann. of Math
    • Ann. of Math
    • Levin, G.1    Van Strien, S.2
  • 20
    • 0040258864 scopus 로고
    • On the borderline of real and complex dynamics
    • Zürich, Switzerland, Birkhäuser Verlag
    • M. Lyubich: On the borderline of real and complex dynamics. In Proceedings of the International Congress of Mathematicians, pages 1203-1215, Zürich, Switzerland, 1994. Birkhäuser Verlag
    • (1994) Proceedings of the International Congress of Mathematicians , pp. 1203-1215
    • Lyubich, M.1
  • 21
    • 84968502739 scopus 로고
    • The Fibonacci unimodal map
    • Apr
    • M. Lyubich, J. Milnor: The Fibonacci unimodal map. J. Amer. Math. Soc., 6(2), 425-457 Apr 1993
    • (1993) J. Amer. Math. Soc. , vol.6 , Issue.2 , pp. 425-457
    • Lyubich, M.1    Milnor, J.2
  • 22
    • 34250112903 scopus 로고
    • Hyperbolicity, sinks and measure in one dimensional dynamics
    • R. Mañé: Hyperbolicity, sinks and measure in one dimensional dynamics. Comm. Math. Phys., 100(4), 495-524 (1985)
    • (1985) Comm. Math. Phys. , vol.100 , Issue.4 , pp. 495-524
    • Mañé, R.1
  • 23
    • 0000848698 scopus 로고
    • On iterated maps of the interval
    • Dynamical Systems: Proceedings 1986-87, Springer-Verlag
    • J. Milnor, W. Thurston: On iterated maps of the interval. In Dynamical Systems: Proceedings 1986-87, pages 465-563. Springer-Verlag, 1988. Lecture Notes in Mathematics 1342
    • (1988) Lecture Notes in Mathematics , vol.1342 , pp. 465-563
    • Milnor, J.1    Thurston, W.2
  • 24
    • 51249183577 scopus 로고
    • Absolutely continuous measures for certain maps of an interval
    • M. Misiurewicz: Absolutely continuous measures for certain maps of an interval. Inst. Hautes Études Sci. Math. Pub., 53, 17-51 (1981)
    • (1981) Inst. Hautes Études Sci. Math. Pub. , vol.53 , pp. 17-51
    • Misiurewicz, M.1
  • 25
    • 0041047071 scopus 로고
    • On some dynamical properties of S-unimodal maps on an interval
    • T. Nowicki: On some dynamical properties of S-unimodal maps on an interval. Fund. Math., 126(1), 27-43 (1985)
    • (1985) Fund. Math. , vol.126 , Issue.1 , pp. 27-43
    • Nowicki, T.1
  • 26
    • 0040329540 scopus 로고
    • Symmetric S-unimodal mappings and positive Liapunov exponents
    • T. Nowicki: Symmetric S-unimodal mappings and positive Liapunov exponents. Ergodic Theory Dynamical Systems, 5, 611-616 (1985)
    • (1985) Ergodic Theory Dynamical Systems , vol.5 , pp. 611-616
    • Nowicki, T.1
  • 27
    • 84974201081 scopus 로고
    • A positive Liapunov exponent for the critical value of an S-unimodal map implies uniform hyperbolicity
    • T. Nowicki: A positive Liapunov exponent for the critical value of an S-unimodal map implies uniform hyperbolicity. Ergodic Theory Dynamical Systems, 8, 425-435 (1988)
    • (1988) Ergodic Theory Dynamical Systems , vol.8 , pp. 425-435
    • Nowicki, T.1
  • 28
    • 0005196176 scopus 로고
    • Some dynamical properties of S-unimodal maps
    • T. Nowicki: Some dynamical properties of S-unimodal maps. Fund. Math., 142(1), 45-57 (1993)
    • (1993) Fund. Math. , vol.142 , Issue.1 , pp. 45-57
    • Nowicki, T.1
  • 29
    • 0039145287 scopus 로고    scopus 로고
    • Topological invariance of the Collet-Eckmann property for S-unimodal maps
    • To appear
    • T. Nowicki, F. Przytycki: Topological invariance of the Collet-Eckmann property for S-unimodal maps. To appear in Fund. Math
    • Fund. Math
    • Nowicki, T.1    Przytycki, F.2
  • 30
    • 84974251975 scopus 로고
    • The conjugacy of collet-Eckmann's map of the interval with the tent map is Hölder continuous
    • T. Nowicki, F. Przytycki: The conjugacy of Collet-Eckmann's map of the interval with the tent map is Hölder continuous. Ergodic Theory Dynamical Systems, 9, 379-388 (1989)
    • (1989) Ergodic Theory Dynamical Systems , vol.9 , pp. 379-388
    • Nowicki, T.1    Przytycki, F.2
  • 31
    • 0000271607 scopus 로고
    • Zeta functions and the periodic orbit structure of hyperbolic dynamics
    • Société Mathématique de France
    • W. Parry, M. Pollicott: Zeta functions and the periodic orbit structure of hyperbolic dynamics, volume 187-188 of Astérisque. Société Mathématique de France, 1990
    • (1990) Astérisque , vol.187-188
    • Parry, W.1    Pollicott, M.2
  • 35
    • 0001273984 scopus 로고
    • Stable orbits and bifurcation of maps of the interval
    • D. Singer: Stable orbits and bifurcation of maps of the interval. SIAM J. Appl. Math., 35(2), 260-267 (1978)
    • (1978) SIAM J. Appl. Math. , vol.35 , Issue.2 , pp. 260-267
    • Singer, D.1
  • 36
    • 84968514104 scopus 로고
    • Differentiable dynamical systems
    • S. Smale: Differentiable dynamical systems. Bull. Amer. Math. Soc., 73, 747-817 (1967)
    • (1967) Bull. Amer. Math. Soc. , vol.73 , pp. 747-817
    • Smale, S.1
  • 37
    • 0039802114 scopus 로고
    • Smooth dynamics on the interval (with an emphasis on quadratic-like maps)
    • T. Bedford and J. Swift, editors, New Directions in Differentiable Dynamical Systems, Cambridge University Press
    • S. van Strien: Smooth dynamics on the interval (with an emphasis on quadratic-like maps). In T. Bedford and J. Swift, editors, New Directions in Differentiable Dynamical Systems, pages 57-119. Cambridge University Press, 1988. London Math. Soc. Lecture Note Ser. 127
    • (1988) London Math. Soc. Lecture Note Ser. , vol.127 , pp. 57-119
    • Van Strien, S.1
  • 38
    • 0001470078 scopus 로고
    • Decay of correlations for certain quadratic maps
    • L.-S. Young: Decay of correlations for certain quadratic maps. Comm. Math. Phys., 146, 123-138 (1992)
    • (1992) Comm. Math. Phys. , vol.146 , pp. 123-138
    • Young, L.-S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.