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Pointwise hyperbolicity implies uniform hyperbolicity
1. | Department of Mathematics, Tufts University, Medford, MA 02155 |
2. | Department of Mathematics, McAllister Building, Pennsylvania State University, University Park, PA 16802 |
3. | Department of Mathematics, Lund Institute of Technology, Lunds Universitet, Box 118, SE-22100 Lund, Sweden |
References:
[1] |
J. F. Alves, V. Araújo and B. Saussol, On the uniform hyperbolicity of some nonuniformly hyperbolic systems, Proc. Amer. Math. Soc., 131 (2003), 1303-1309.
doi: 10.1090/S0002-9939-02-06857-0. |
[2] |
L. Barreira and Y. Pesin, Nonuniform Hyperbolicity. Dynamics of Systems with Nonzero Lyapunov Exponents, Encyclopedia of Mathematics and its Applications, 115, Cambridge University Press, Cambridge, 2007. |
[3] |
Y. Cao, Non-zero Lyapunov exponents and uniform hyperbolicity, Nonlinearity, 16 (2003), 1473-1479.
doi: 10.1088/0951-7715/16/4/316. |
[4] |
Y. Cao, S. Luzzatto and I. Rios, A minimum principle for Lyapunov exponents and a higher-dimensional version of a theorem of Mañé, Qual. Theory Dyn. Syst., 5 (2004), 261-273.
doi: 10.1007/BF02972681. |
[5] |
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.
doi: 10.3934/dcds.2006.15.61. |
[6] |
A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Encyclopedia of Mathematics and its Applications, 54, Cambridge University Press, Cambridge, 1995. |
[7] |
R. Mañé, Quasi-Anosov diffeomorphisms and hyperbolic manifolds, Trans. Amer. Math. Soc., 229 (1977), 351-370. |
[8] |
R. Sacker and G. Sell, Existence of dichotomies and invariant splittings for linear differential systems. I, J. Differential Equations, 15 (1974), 429-458.
doi: 10.1016/0022-0396(74)90067-9. |
show all references
References:
[1] |
J. F. Alves, V. Araújo and B. Saussol, On the uniform hyperbolicity of some nonuniformly hyperbolic systems, Proc. Amer. Math. Soc., 131 (2003), 1303-1309.
doi: 10.1090/S0002-9939-02-06857-0. |
[2] |
L. Barreira and Y. Pesin, Nonuniform Hyperbolicity. Dynamics of Systems with Nonzero Lyapunov Exponents, Encyclopedia of Mathematics and its Applications, 115, Cambridge University Press, Cambridge, 2007. |
[3] |
Y. Cao, Non-zero Lyapunov exponents and uniform hyperbolicity, Nonlinearity, 16 (2003), 1473-1479.
doi: 10.1088/0951-7715/16/4/316. |
[4] |
Y. Cao, S. Luzzatto and I. Rios, A minimum principle for Lyapunov exponents and a higher-dimensional version of a theorem of Mañé, Qual. Theory Dyn. Syst., 5 (2004), 261-273.
doi: 10.1007/BF02972681. |
[5] |
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.
doi: 10.3934/dcds.2006.15.61. |
[6] |
A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Encyclopedia of Mathematics and its Applications, 54, Cambridge University Press, Cambridge, 1995. |
[7] |
R. Mañé, Quasi-Anosov diffeomorphisms and hyperbolic manifolds, Trans. Amer. Math. Soc., 229 (1977), 351-370. |
[8] |
R. Sacker and G. Sell, Existence of dichotomies and invariant splittings for linear differential systems. I, J. Differential Equations, 15 (1974), 429-458.
doi: 10.1016/0022-0396(74)90067-9. |
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