Invariant families of cones and Lyapunov exponents

From MaRDI portal
Publication:3700486

DOI10.1017/S0143385700002807zbMath0578.58033MaRDI QIDQ3700486

Maciej P. Wojtkowski

Publication date: 1985

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)




Related Items (73)

Principles for the design of billiards with nonvanishing Lyapunov exponentsPositive metric entropy in nondegenerate nearly integrable systemsTrack billiardsUnnamed ItemLyapunov sequences for exponential dichotomiesQuadratic Lyapunov functions and nonuniform exponential dichotomiesLyapunov functions for strong exponential contractionsSemi-focusing billiards: HyperbolicityPotentials on the two-torus for which the Hamiltonian flow is ergodicConditional proof of the Boltzmann-Sinai ergodic hypothesisBernoulli automorphisms of finitely generated free MV-algebrasChaotic properties of the elliptical stadiumUniform hyperbolicity in nonflat billiardsHomoclinic orbits and entropy for three-dimensional flowsDifferentiability of Lyapunov exponentsOn the mathematical transport theory in microporous media: the billiard approachThe symplectic semigroup and Riccati differential equationsLyapunov functions for strong exponential dichotomiesDetecting invariant expanding cones for generating word sets to identify chaos in piecewise-linear mapsHyperbolicity and abundance of elliptical islands in annular billiardsThe Weil-Petersson geodesic flow is ergodicMarked length spectral determination of analytic chaotic billiards with axial symmetriesWeyl-flow and the conformally symplectic structure of thermostatted billiards: the problem of the hyperbolicityHomoclinic and heteroclinic intersections for lemon billiardsEscape rates and physically relevant measures for billiards with small holesNonuniform exponential dichotomies and Lyapunov functionsBernoulli property for some hyperbolic billiardsThe basic ergodic theorems, yet againThe density of linear symplectic cocycles with simple Lyapunov spectrum in \({\mathcal G}_{IC}(X, \mathrm{SL}(2,\mathbb R))\)Infinitesimal Lyapunov functions for singular flowsA system of one-dimensional balls with gravityOn soft billiard systemsA Bernoulli toral linked twist map without positive Lyapunov exponentsCLASSICAL AND QUANTUM FEATURES OF THE MIXMASTER SINGULARITYAnatole KatokPositive top Lyapunov exponent via invariant cones: single trajectoriesHyperbolicity of asymmetric lemon billiards *Gibbs measures for fibred systemsNonuniform dichotomies via Lyapunov functionsAdapted Metrics for Codimension One Singular Hyperbolic FlowsThe ergodicity of a Hamiltonian system of two particles in an external fieldUsing integrability to produce chaos: Billiards with positive entropyHyperbolicity and integral expression of the Lyapunov exponents for linear cocyclesHyperbolic billiards with nearly flat focusing boundaries. I.Singular hyperbolicity and sectional Lyapunov exponents of various ordersErgodic systems of \(n\) balls in a billiard tableThe characteristic exponents of the falling ball modelOn the Bernoulli property of planar hyperbolic billiardsOn random linear dynamical systems in a Banach space. I: Multiplicative ergodic theorem and Krein-Rutman type theoremsTransport processes from mechanics: minimal and simplest modelsLyapunov functions and cone familiesIsospectral deformations of random Jacobi operatorsBilliard dynamics: An updated survey with the emphasis on open problemsMultidimensional hyperbolic billiardsDecay of correlations for billiards with flat points I: channel effectsDecay of correlations for billiards with flat points II: cusps effectA constructive approach to robust chaos using invariant manifolds and expanding conesSome remarks on the problem of ergodicity of the standard mapSmoothness of the carrying simplex for discrete-time competitive dynamical systems: A characterization of neat embeddingExponential decay of correlations for randomly chosen hyperbolic toral automorphismsNonuniform exponential contractions and Lyapunov sequencesFinite Gauss measure on the space of interval exchange transformations. Lyapunov exponentsQuantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalitiesEntropy, Lyapunov exponents, and mean free path for billiardsComplete hyperbolicity in Hamiltonian systems with linear potential and elastic collisionsBook Review: Chaotic billiardsA local ergodic theorem for non-uniformly hyperbolic symplectic maps with singularitiesMixing rates for symplectic almost Anosov mapsSmooth dependence of fixed points of HamiltoniansLie semigroup associated to the symmetric coneLyapunov sequences for exponential trichotomiesSpectral theorem for convex monotone homogeneous maps, and ergodic controlDominated splitting for exterior powers and singular hyperbolicity



Cites Work


This page was built for publication: Invariant families of cones and Lyapunov exponents