What are Lyapunov exponents, and why are they interesting?
DOI10.1090/bull/1552zbMath1390.37041arXiv1608.02843OpenAlexW2491160177MaRDI QIDQ3178749
Publication date: 20 December 2016
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1608.02843
Ergodicity, mixing, rates of mixing (37A25) Characteristic and Lyapunov exponents of ordinary differential equations (34D08) Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Genericity of nonuniform hyperbolicity in dimension 3
- Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow
- Every flat surface is Birkhoff and Oseledets generic in almost every direction
- Absolute continuity, Lyapunov exponents and rigidity. I: Geodesic flows
- Diffeomorphisms with positive metric entropy
- On the regularization of conservative maps
- The Lyapunov exponents of generic volume-preserving and symplectic maps
- Invariant measures and the set of exceptions to Littlewood's conjecture
- Global theory of one-frequency Schrödinger operators
- Extremal Lyapunov exponents: an invariance principle and applications
- The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
- Exponential dichotomy, rotation number, and linear differential operators with bounded coefficients
- Ergodicity of billiard flows and quadratic differentials
- The Teichmüller geodesic flow
- Propriétés de contraction d'un semi-groupe de matrices inversibles. Coefficients de Liapunoff d'un produit de matrices aléatoires indépendantes. (Contraction properties of a semigoup of invertible matrices. Lyapunov coefficient of a product of independent random matrices)
- Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
- Zero measure spectrum for the almost Mathieu operator
- Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential
- Généricité d'exposants de Lyapunov non-nuls pour des produits déterministes de matrices. (Genericity of non-zero Lyapunov exponents for deterministic products of matrices)
- Deviation of ergodic averages for area-preserving flows on surfaces of higher genus
- Pathological foliations and removable zero exponents
- Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture
- Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents
- The Ten Martini problem
- The metric entropy of diffeomorphisms. II: Relations between entropy, exponents and dimension
- Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles
- Simplicity of Lyapunov spectra: a sufficient criterion
- Invariant measures and arithmetic unique ergodicity. Appendix by E. Lindenstrauss and D. Rudolph
- Measure-preserving homeomorphisms and metrical transitivity
- Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms
- Lyapunov indices of a product of random matrices
- C1-generic symplectic diffeomorphisms: partial hyperbolicity and zero centre Lyapunov exponents
- CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
- Every compact manifold carries a completely hyperbolic diffeomorphism
- Dynamics and spectral theory of quasi-periodic Schrödinger-type operators
- Genericity of zero Lyapunov exponents
- Barycentric subdivision of triangles and semigroups of Möbius maps
- Lyapunov exponents with multiplicity 1 for deterministic products of matrices
- Lectures on Lyapunov Exponents
- Products of Random Matrices
- Noncommuting Random Products
- Harmonic analysis.
- On nonperturbative localization with quasi-periodic potential.