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The Multiplicative Ergodic Theorem
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Lyapunov Exponents and Smooth Ergodic Theory
Introduction Lyapunov stability theory of differential equations Elements of nonuniform hyperbolic theory Examples of nonuniformly hyperbolic systems Local manifold theory Ergodic properties ofExpand
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Sets of “Non-typical” points have full topological entropy and full Hausdorff dimension
For subshifts of finite type, conformal repellers, and conformal horseshoes, we prove that the set of points where the pointwise dimensions, local entropies, Lyapunov exponents, and Birkhoff averagesExpand
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Stability Of Nonautonomous Differential Equations
Main theme of this volume is the stability of nonautonomous differential equations, with emphasis on the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, theExpand
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Variational principles and mixed multifractal spectra
We establish a " conditional " variational principle, which unifies and extends many results in the multifractal analysis of dynam-ical systems. Namely, instead of considering several quantities ofExpand
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Nonuniform Hyperbolicity: Dynamics of Systems with Nonzero Lyapunov Exponents
Part I. Linear Theory: 1. The concept of nonuniform hyperbolicity 2. Lyapunov exponents for linear extensions 3. Regularity of cocycles 4. Methods for estimating exponents 5. The derivative cocycleExpand
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Hausdorff Dimension of Measures¶via Poincaré Recurrence
Abstract: We study the quantitative behavior of Poincaré recurrence. In particular, for an equilibrium measure on a locally maximal hyperbolic set of a C1+α diffeomorphism f, we show that theExpand
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Dimension and Recurrence in Hyperbolic Dynamics
Basic Notions.- Basic Notions.- Dimension Theory.- Dimension Theory and Thermodynamic Formalism.- Repellers and Hyperbolic Sets.- Measures of Maximal Dimension.- Multifractal Analysis: Core Theory.-Expand
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Dimension and product structure of hyperbolic measures
We prove that every hyperbolic measure invariant under a C 1+fi difieomorphism of a smooth Riemannian manifold possesses asymptotically \almost" local product structure, i.e., its density can beExpand
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Polynomial growth rates
Abstract We consider linear equations v ′ = A ( t ) v with a polynomial asymptotic behavior, that can be stable, unstable and central. We show that this behavior is exhibited by a large class ofExpand
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