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Publications Influence

Lyapunov Exponents and Smooth Ergodic Theory

- L. Barreira, Y. Pesin
- Mathematics
- 2002

Introduction Lyapunov stability theory of differential equations Elements of nonuniform hyperbolic theory Examples of nonuniformly hyperbolic systems Local manifold theory Ergodic properties of… Expand

286 21- PDF

Sets of “Non-typical” points have full topological entropy and full Hausdorff dimension

- L. Barreira, J. Schmeling
- Mathematics
- 1 December 2000

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 averages… Expand

274 18

Stability Of Nonautonomous Differential Equations

- L. Barreira, C. Valls
- Mathematics
- 12 December 2007

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, the… Expand

185 16

Variational principles and mixed multifractal spectra

- L. Barreira, B. Saussol
- Mathematics
- 6 June 2001

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 of… Expand

110 14- PDF

Nonuniform Hyperbolicity: Dynamics of Systems with Nonzero Lyapunov Exponents

- L. Barreira, Y. Pesin
- Mathematics
- 2007

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 cocycle… Expand

188 13- PDF

Hausdorff Dimension of Measures¶via Poincaré Recurrence

- L. Barreira, B. Saussol
- Mathematics
- 1 May 2001

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 the… Expand

122 9- PDF

Dimension and Recurrence in Hyperbolic Dynamics

- L. Barreira
- Mathematics
- 27 August 2008

Basic Notions.- Basic Notions.- Dimension Theory.- Dimension Theory and Thermodynamic Formalism.- Repellers and Hyperbolic Sets.- Measures of Maximal Dimension.- Multifractal Analysis: Core Theory.-… Expand

102 9

Dimension and product structure of hyperbolic measures

- L. Barreira, Y. Pesin, J. Schmeling
- Mathematics
- 1 May 1999

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 be… Expand

154 8- PDF

Polynomial growth rates

- L. Barreira, C. Valls
- Mathematics
- 1 December 2009

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 of… Expand

42 8