Persistent non-statistical dynamics in one-dimensional maps

DOI10.1007/s00220-024-04957-0arXiv2302.11411OpenAlexW4394594601MaRDI QIDQ6125785

Douglas Coates, Stefano Luzzatto

Publication date: 11 April 2024

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2302.11411

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Dynamical systems involving maps of the interval (37E05) Dynamical systems involving one-parameter continuous families of measure-preserving transformations (37A10) Dynamical systems with singularities (billiards, etc.) (37C83)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Rare events for the Manneville-Pomeau map
• Linear response for intermittent maps
• Mixing rates for intermittent maps of high exponent
• Renormalization, thermodynamic formalism and quasi-crystals in subshifts
• The geometric approach for constructing Sinai-Ruelle-Bowen measures
• Characterization of weak convergence of Birkhoff sums for Gibbs-Markov maps
• Linear response in the intermittent family: differentiation in a weighted \(C^0\)-norm
• Geometric Lorenz flows with historic behavior
• Takens' last problem and existence of non-trivial wandering domains
• Transformations on [0,1 with infinite invariant measures]
• Quadratic maps without asymptotic measure
• Invariant measures for interval maps with critical points and singularities
• First return map and invariant measures
• Estimates of the invariant densities of endomorphisms with indifferent fixed points
• Absolutely continuous invariant measures for piecewise real-analytic expanding maps on the plane
• The invariant densities for maps modeling intermittency.
• Almost sure rates of mixing for random intermittent maps
• A limit theorem for the Perron-Frobenius operator of transformations on [0,1 with indifferent fixed points]
• First and higher order uniform dual ergodic theorems for dynamical systems with infinite measure
• Multifractal analysis of Lyapunov exponent for continued fraction and Manneville-Pomeau transformations and applications to diophantine approximation
• Empirical measures of partially hyperbolic attractors
• Anomalous time-scaling of extreme events in infinite systems and Birkhoff sums of infinite observables
• Measures of maximal entropy for surface diffeomorphisms
• Historic behaviour vs. physical measures for irrational flows with multiple stopping points
• Abundance of observable Lyapunov irregular sets
• Emergence via non-existence of averages
• SRB measures of singular hyperbolic attractors
• Non-statistical rational maps
• The pressure function for infinite equilibrium measures
• The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics
• SRB measures for partially hyperbolic systems whose central direction is weakly expanding
• Physical measures for partially hyperbolic surface endomorphisms
• Maximal inequalities of weak type
• Markov structures and decay of correlations for non-uniformly expanding dynamical systems
• Abundance of wild historic behavior
• Exact bounds for the polynomial decay of correlation, 1/fnoise and the CLT for the equilibrium state of a non-Hölder potential
• Linear response for intermittent maps with summable and nonsummable decay of correlations
• On statistical attractors and the convergence of time averages
• Spectral degeneracy and escape dynamics for intermittent maps with a hole
• Nonuniformly Hyperbolic Attractors
• Large deviations for intermittent maps
• STATISTICAL PROPERTIES OF ONE-DIMENSIONAL MAPS WITH CRITICAL POINTS AND SINGULARITIES
• Decay of correlations for invertible maps with non-Hölder observables
• Statistical properties of intermittent maps with unbounded derivative
• Large and moderate deviations for slowly mixing dynamical systems
• On the Existence of Invariant Measures for Piecewise Monotonic Transformations
• A Measure Associated with Axiom-A Attractors
• Ergodic structure and invariant densities of non-Markovian interval maps with indifferent fixed points
• A probabilistic approach to intermittency
• Heteroclinic attractors: Time averages and moduli of topological conjugacy
• Nonexistence of SBR measures for some diffeomorphisms that are ‘Almost Anosov’
• LOCAL LIMIT THEOREMS FOR PARTIAL SUMS OF STATIONARY SEQUENCES GENERATED BY GIBBS–MARKOV MAPS
• Absolutely continuous invariant probability measures for arbitrary expanding piecewise $\mathbb{R}$-analytic mappings of the plane
• The connection between time averages and minimal attractors
• Ergodic properties of infinite measure-preserving interval maps with indifferent fixed points
• The asymptotics of the Perron-Frobenius operator of a class of interval maps preserving infinite measures
• Exact C^∞covering maps of the circle without (weak) limit measure
• Historic behaviour for nonautonomous contraction mappings
• A rigorous computational approach to linear response
• Central limit theorems for sequential and random intermittent dynamical systems
• Relations between natural and observable measures
• Statistical properties of long return times in type I intermittency
• STABLE LIMITS FOR PROBABILITY PRESERVING MAPS WITH INDIFFERENT FIXED POINTS
• Completely mixing maps without limit measure
• Coexistence of invariant sets with and without SRB measures in Hénon family
• Sojourn times in small neighborhoods of indifferent fixed points of one-dimensional dynamical systems
• Invariant densities for intermittent maps with critical points
• Limit theorems for wobbly interval intermittent maps
• Univariate Stable Distributions
• Historic behavior in nonhyperbolic homoclinic classes
• Open questions leading to a global perspective in dynamics (2008Nonlinearity21 T37–43)
• Improved mixing rates for infinite measure-preserving systems
• On Takens’ last problem: tangencies and time averages near heteroclinic networks
• ACIM for random intermittent maps: existence, uniqueness and stochastic stability
• On stochastic stability of expanding circle maps with neutral fixed points
• Orbits with historic behaviour, or non-existence of averages
• Open questions leading to a global perspective in dynamics
• Sinai–Ruelle–Bowen measures for weakly expanding maps
• An example of non-coincidence of minimal and statistical attractors
• SOME SMOOTH ERGODIC SYSTEMS
• GIBBS MEASURES IN ERGODIC THEORY
• ASYMPTOTIC DISTRIBUTIONS AND LARGE DEVIATIONS FOR ITERATED MAPS WITH AN INDIFFERENT FIXED POINT
• Occupation times of sets of infinite measure for ergodic transformations
• Emergence of wandering stable components
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• A note on the Borel-Cantelli lemma
• Absolutely continuous invariant measures for expanding piecewise linear maps
• Phase transitions for countable Markov shifts
• Historic and physical wandering domains for wild blender-horseshoes
• Doubly intermittent full branch maps with critical points and singularities
• SRB measures for \(C^{\infty}\) surface diffeomorphisms