International Journal of Bifurcation and Chaos, ISSN 0218-1274, 07/2016, Volume 26, Issue 8, p. 1650131

This paper introduces a class of polynomial maps in Euclidean spaces, investigates the conditions under which there exist Smale horseshoes and uniformly...

Smale horseshoe | chaos | polynomial map | Attractor | uniformly hyperbolic set | DIFFEOMORPHISMS | HENON MAPS | MULTIDISCIPLINARY SCIENCES | JACOBIAN CONJECTURE | C-2 | COUPLED-EXPANDING MAPS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | HYPERBOLICITY | DYNAMICS

Smale horseshoe | chaos | polynomial map | Attractor | uniformly hyperbolic set | DIFFEOMORPHISMS | HENON MAPS | MULTIDISCIPLINARY SCIENCES | JACOBIAN CONJECTURE | C-2 | COUPLED-EXPANDING MAPS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | HYPERBOLICITY | DYNAMICS

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 10/2017, Volume 37, Issue 10, pp. 5085 - 5104

We prove that any c(1)+(BV) degree d >= 2 circle covering h having all periodic orbits weakly expanding, is conjugate by a C-1+(BV) diffeomorphism to a...

Circle covering | Smooth conjugacy | Parabolic external map | Parabolic-like map | Metric expanding | MATHEMATICS | MATHEMATICS, APPLIED | metric expanding | ONE-DIMENSIONAL DYNAMICS | smooth conjugacy | parabolic-like map | MAPPINGS | parabolic external map | Mathematics - Dynamical Systems

Circle covering | Smooth conjugacy | Parabolic external map | Parabolic-like map | Metric expanding | MATHEMATICS | MATHEMATICS, APPLIED | metric expanding | ONE-DIMENSIONAL DYNAMICS | smooth conjugacy | parabolic-like map | MAPPINGS | parabolic external map | Mathematics - Dynamical Systems

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 1/2017, Volume 166, Issue 1, pp. 114 - 136

We consider semigroups of Ruelle-expanding maps, parameterized by random walks on the free semigroup, with the aim of examining their complexity and exploring...

Secondary: 37D20 | Theoretical, Mathematical and Computational Physics | Semigroup actions | Quantum Physics | 37D35 | Physics | Statistical Physics and Dynamical Systems | Expanding maps | 37B40 | 37C85 | Physical Chemistry | Primary: 37B05 | Skew-product | Equilibrium states | Zeta function | SATISFYING EXPANSIVENESS | VARIATIONAL PRINCIPLE | SPECIFICATION | PHYSICS, MATHEMATICAL | PERIODIC POINTS | THERMODYNAMIC FORMALISM | GIBBS | TRANSFORMATIONS | Thermodynamics | Mathematics - Dynamical Systems

Secondary: 37D20 | Theoretical, Mathematical and Computational Physics | Semigroup actions | Quantum Physics | 37D35 | Physics | Statistical Physics and Dynamical Systems | Expanding maps | 37B40 | 37C85 | Physical Chemistry | Primary: 37B05 | Skew-product | Equilibrium states | Zeta function | SATISFYING EXPANSIVENESS | VARIATIONAL PRINCIPLE | SPECIFICATION | PHYSICS, MATHEMATICAL | PERIODIC POINTS | THERMODYNAMIC FORMALISM | GIBBS | TRANSFORMATIONS | Thermodynamics | Mathematics - Dynamical Systems

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2016, Volume 435, Issue 1, pp. 492 - 507

Let C1(M) be the space of differentiable maps of a closed C∞ manifold M endowed with the C1-topology, and let f∈C1(M). The purpose of this paper is to...

Expanding maps | Positively expansive maps | Measure-expansive | DIFFEOMORPHISMS | MATHEMATICS | MATHEMATICS, APPLIED | STABILITY | ENDOMORPHISMS

Expanding maps | Positively expansive maps | Measure-expansive | DIFFEOMORPHISMS | MATHEMATICS | MATHEMATICS, APPLIED | STABILITY | ENDOMORPHISMS

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 02/2019, Volume 67, pp. 272 - 289

•Necessary and sufficient conditions to have robust chaotic dynamics in the whole interval for expanding one-dimensional discontinuous maps are given for the...

1D non-expanding maps | Lorenz maps | 1D expanding maps | 1D discontinuos maps | Full chaos | MATHEMATICS, APPLIED | BIFURCATIONS | INVARIANTS | PHYSICS, FLUIDS & PLASMAS | CLASSIFICATION | PHYSICS, MATHEMATICAL | ATTRACTORS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PENDULUM | DYNAMICS | SYSTEMS | IMPACTS | TRANSFORMATIONS

1D non-expanding maps | Lorenz maps | 1D expanding maps | 1D discontinuos maps | Full chaos | MATHEMATICS, APPLIED | BIFURCATIONS | INVARIANTS | PHYSICS, FLUIDS & PLASMAS | CLASSIFICATION | PHYSICS, MATHEMATICAL | ATTRACTORS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PENDULUM | DYNAMICS | SYSTEMS | IMPACTS | TRANSFORMATIONS

Journal Article

Advances in Mathematics, ISSN 0001-8708, 02/2019, Volume 343, pp. 712 - 755

Let Tf:[0,1]→[0,1] be an expanding Lorenz map, this means Tfx:=f(x)(mod 1) where f:[0,1]→[0,2] is a strictly increasing map satisfying inff′>1. Then Tf has...

Expanding map | Renormalizable map | Topological mixing | Locally eventually onto | Topological transitivity | Lorenz map | MATHEMATICS | INTRINSIC ERGODICITY | DYNAMICS | CLASSIFICATION | PIECEWISE MONOTONIC TRANSFORMATIONS | RENORMALIZATION

Expanding map | Renormalizable map | Topological mixing | Locally eventually onto | Topological transitivity | Lorenz map | MATHEMATICS | INTRINSIC ERGODICITY | DYNAMICS | CLASSIFICATION | PIECEWISE MONOTONIC TRANSFORMATIONS | RENORMALIZATION

Journal Article

Nonlinearity, ISSN 0951-7715, 05/2017, Volume 30, Issue 7, pp. 2737 - 2751

How can one change a system, in order to change its statistical properties in a prescribed way? In this note we consider a control problem related to the...

linear response | 49N05 | optimal control | 37N35 | expanding maps Mathematics Subject Classification numbers: 37C30 | MATHEMATICS, APPLIED | LINEAR-RESPONSE | expanding maps | SYSTEMS | DIFFERENTIATION | FLOWS | PHYSICS, MATHEMATICAL | SRB STATES | Mathematics - Dynamical Systems

linear response | 49N05 | optimal control | 37N35 | expanding maps Mathematics Subject Classification numbers: 37C30 | MATHEMATICS, APPLIED | LINEAR-RESPONSE | expanding maps | SYSTEMS | DIFFERENTIATION | FLOWS | PHYSICS, MATHEMATICAL | SRB STATES | Mathematics - Dynamical Systems

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 04/2019, Volume 39, Issue 4, pp. 1779 - 1797

A typical approach to analysing statistical properties of expanding maps is to show spectral gaps of associated transfer operators in adapted function spaces....

Expanding map | Quasi-compactness | Littlewood-Paley decomposition | Transfer operator | Besov space | MATHEMATICS | expanding map | TRANSFER OPERATORS | MATHEMATICS, APPLIED | quasi-compactness | DETERMINANTS | HOLDER | GAP | EXTENSION

Expanding map | Quasi-compactness | Littlewood-Paley decomposition | Transfer operator | Besov space | MATHEMATICS | expanding map | TRANSFER OPERATORS | MATHEMATICS, APPLIED | quasi-compactness | DETERMINANTS | HOLDER | GAP | EXTENSION

Journal Article

Ergodic Theory and Dynamical Systems, ISSN 0143-3857, 09/2018, Volume 38, Issue 6, pp. 2036 - 2061

We study the dependence of the topological entropy of piecewise monotonic maps with holes under perturbations, for example sliding a hole of fixed size at...

EXPANDING MAPS | MATHEMATICS | MATHEMATICS, APPLIED | INVARIANT-MEASURES | DYNAMICAL-SYSTEMS | SETS | CONVERGENCE | TRANSFORMATIONS | CIRCLE | Chaos theory | Entropy | Dependence

EXPANDING MAPS | MATHEMATICS | MATHEMATICS, APPLIED | INVARIANT-MEASURES | DYNAMICAL-SYSTEMS | SETS | CONVERGENCE | TRANSFORMATIONS | CIRCLE | Chaos theory | Entropy | Dependence

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 09/2017, Volume 37, Issue 9, pp. 5049 - 5063

In this paper we prove that a postcritically finite rational map with non-empty Fatou set is Thurston equivalent to an expanding Thurston map if and only if...

Low dimensional dynamics | Rational maps | Sierpiński carpet Julia sets | Thurston equivalent | Expanding Thurston maps | MATHEMATICS | MATHEMATICS, APPLIED | DYNAMICS | rational maps | expanding Thurston maps | CURVES | Sierpinski carpet Julia sets | thurston equivalent

Low dimensional dynamics | Rational maps | Sierpiński carpet Julia sets | Thurston equivalent | Expanding Thurston maps | MATHEMATICS | MATHEMATICS, APPLIED | DYNAMICS | rational maps | expanding Thurston maps | CURVES | Sierpinski carpet Julia sets | thurston equivalent

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 07/2017, Volume 145, Issue 7, pp. 3057 - 3068

We present sufficient conditions for the (strong) statistical stability of some classes of multidimensional piecewise expanding maps. As a consequence we get...

Piecewise expanding maps | Physical measures | Statistical stability | MATHEMATICS, APPLIED | BIFURCATIONS | C-2 TRANSFORMATIONS | statistical stability | physical measures | MATHEMATICS | CONTINUOUS INVARIANT-MEASURES | 3-DIMENSIONAL DISSIPATIVE DIFFEOMORPHISMS | PLANE | EXPANSION | DYNAMICS | HOMOCLINIC TANGENCIES

Piecewise expanding maps | Physical measures | Statistical stability | MATHEMATICS, APPLIED | BIFURCATIONS | C-2 TRANSFORMATIONS | statistical stability | physical measures | MATHEMATICS | CONTINUOUS INVARIANT-MEASURES | 3-DIMENSIONAL DISSIPATIVE DIFFEOMORPHISMS | PLANE | EXPANSION | DYNAMICS | HOMOCLINIC TANGENCIES

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 1/2018, Volume 170, Issue 2, pp. 221 - 253

For real analytic expanding interval maps, a novel method is given for rigorously approximating the diffusion coefficient of real analytic observables. As a...

Expanding map | Ergodic theory | Dynamical Systems | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Quantum Physics | Diffusion coefficient | Physics | Statistical Physics and Dynamical Systems | PHYSICS, MATHEMATICAL

Expanding map | Ergodic theory | Dynamical Systems | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Quantum Physics | Diffusion coefficient | Physics | Statistical Physics and Dynamical Systems | PHYSICS, MATHEMATICAL

Journal Article

Ergodic Theory and Dynamical Systems, ISSN 0143-3857, 05/2018, Volume 38, Issue 3, pp. 1168 - 1200

For a strongly dissipative Henon-like map at the first bifurcation parameter at which the uniform hyperbolicity is destroyed by the formation of tangencies...

MULTIFRACTAL ANALYSIS | DIFFEOMORPHISMS | MATHEMATICS | MATHEMATICS, APPLIED | CONFORMAL EXPANDING MAPS | EQUILIBRIUM MEASURES | HYPERBOLICITY | SYSTEMS | FORMALISM | PARABOLIC HORSESHOES | STRANGE ATTRACTORS | TOPOLOGICAL-ENTROPY | Bifurcations | Decomposition | Maps | Chaos theory | Liapunov exponents | Fractal analysis

MULTIFRACTAL ANALYSIS | DIFFEOMORPHISMS | MATHEMATICS | MATHEMATICS, APPLIED | CONFORMAL EXPANDING MAPS | EQUILIBRIUM MEASURES | HYPERBOLICITY | SYSTEMS | FORMALISM | PARABOLIC HORSESHOES | STRANGE ATTRACTORS | TOPOLOGICAL-ENTROPY | Bifurcations | Decomposition | Maps | Chaos theory | Liapunov exponents | Fractal analysis

Journal Article

Ergodic Theory and Dynamical Systems, ISSN 0143-3857, 08/2016, Volume 36, Issue 5, pp. 1441 - 1493

We study the dimension spectrum of Lyapunov exponents for multimodal maps of the interval and their generalizations. We also present related results for...

EXPANDING MAPS | JULIA SETS | MATHEMATICS | TOPOLOGICAL INVARIANCE | MATHEMATICS, APPLIED | INTERVAL MAPS | RATIONAL FUNCTIONS | NONUNIFORM HYPERBOLICITY | CONFORMAL MEASURES | S-UNIMODAL MAPS | COLLET-ECKMANN MAPS | MULTIFRACTAL SPECTRA | Dynamical systems | Spectrum analysis | Maps | Intervals | Lyapunov exponents | Ergodic processes | Mathematics - Dynamical Systems

EXPANDING MAPS | JULIA SETS | MATHEMATICS | TOPOLOGICAL INVARIANCE | MATHEMATICS, APPLIED | INTERVAL MAPS | RATIONAL FUNCTIONS | NONUNIFORM HYPERBOLICITY | CONFORMAL MEASURES | S-UNIMODAL MAPS | COLLET-ECKMANN MAPS | MULTIFRACTAL SPECTRA | Dynamical systems | Spectrum analysis | Maps | Intervals | Lyapunov exponents | Ergodic processes | Mathematics - Dynamical Systems

Journal Article

Nonlinearity, ISSN 0951-7715, 04/2018, Volume 31, Issue 5, pp. 2252 - 2280

We prove a fiberwise almost sure invariance principle for random piecewise expanding transformations in one and higher dimensions using recent developments on...

almost sure invariance principle | random dynamical systems | piecewise expanding maps | MATHEMATICS, APPLIED | DECAY | DYNAMICAL-SYSTEMS | LIMIT-THEOREMS | LASOTA-YORKE MAPS | MONOTONIC TRANSFORMATIONS | PHYSICS, MATHEMATICAL | Mathematics - Dynamical Systems | Dynamical Systems | Mathematics

almost sure invariance principle | random dynamical systems | piecewise expanding maps | MATHEMATICS, APPLIED | DECAY | DYNAMICAL-SYSTEMS | LIMIT-THEOREMS | LASOTA-YORKE MAPS | MONOTONIC TRANSFORMATIONS | PHYSICS, MATHEMATICAL | Mathematics - Dynamical Systems | Dynamical Systems | Mathematics

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 4/2017, Volume 351, Issue 2, pp. 775 - 835

If a system mixes too slowly, putting a hole in it can completely destroy the richness of the dynamics. Here we study this instability for a class of...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | THERMODYNAMIC FORMALISM | MULTIFRACTAL ANALYSIS | EXPANDING MAPS | CONDITIONALLY INVARIANT-MEASURES | RATES | DYNAMICAL-SYSTEMS | MARKOV EXTENSIONS | PROBABILITY-MEASURES | GIBBS MEASURES | PHYSICS, MATHEMATICAL | PHYSICAL MEASURES | Thermodynamics | Mathematics - Dynamical Systems

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | THERMODYNAMIC FORMALISM | MULTIFRACTAL ANALYSIS | EXPANDING MAPS | CONDITIONALLY INVARIANT-MEASURES | RATES | DYNAMICAL-SYSTEMS | MARKOV EXTENSIONS | PROBABILITY-MEASURES | GIBBS MEASURES | PHYSICS, MATHEMATICAL | PHYSICAL MEASURES | Thermodynamics | Mathematics - Dynamical Systems

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/2018, Volume 146, Issue 5, pp. 2103 - 2116

We study non-stationary stochastic processes arising from sequential dynamical systems built on maps with a neutral fixed point and prove the existence of...

Extreme value theory | Intermittent maps | Sequential dynamical systems | Non-stationarity | INTERVAL | intermittent maps | MATHEMATICS, APPLIED | LINEAR-RESPONSE | Extreme Value Theory | EXPANDING DYNAMICAL-SYSTEMS | STABILITY | MATHEMATICS | HITTING TIME STATISTICS | RATES | LIMIT-THEOREMS | sequential dynamical systems | Dynamical Systems | Mathematics

Extreme value theory | Intermittent maps | Sequential dynamical systems | Non-stationarity | INTERVAL | intermittent maps | MATHEMATICS, APPLIED | LINEAR-RESPONSE | Extreme Value Theory | EXPANDING DYNAMICAL-SYSTEMS | STABILITY | MATHEMATICS | HITTING TIME STATISTICS | RATES | LIMIT-THEOREMS | sequential dynamical systems | Dynamical Systems | Mathematics

Journal Article

Nonlinearity, ISSN 0951-7715, 02/2015, Volume 28, Issue 2, pp. 407 - 434

For a two-dimensional extension of the classical one-dimensional family of tent maps, we prove the existence of an open set of parameters for which the...

piecewise linear maps | invariant measures | strange attractors | EXPANDING MAPS | ATTRACTORS | MATHEMATICS, APPLIED | CONTINUOUS INVARIANT-MEASURES | BIFURCATIONS | 3-DIMENSIONAL DISSIPATIVE DIFFEOMORPHISMS | PHYSICS, MATHEMATICAL | HOMOCLINIC TANGENCIES | TRANSFORMATIONS | Nonlinear dynamics | Strange attractors | Maps | Transformations (mathematics) | Nonlinearity | Orbits | Two dimensional | Invariants

piecewise linear maps | invariant measures | strange attractors | EXPANDING MAPS | ATTRACTORS | MATHEMATICS, APPLIED | CONTINUOUS INVARIANT-MEASURES | BIFURCATIONS | 3-DIMENSIONAL DISSIPATIVE DIFFEOMORPHISMS | PHYSICS, MATHEMATICAL | HOMOCLINIC TANGENCIES | TRANSFORMATIONS | Nonlinear dynamics | Strange attractors | Maps | Transformations (mathematics) | Nonlinearity | Orbits | Two dimensional | Invariants

Journal Article

Ergodic Theory and Dynamical Systems, ISSN 0143-3857, 2014, Volume 34, Issue 4, pp. 1116 - 1141

For a positive measure set of non-uniformly expanding quadratic maps on the interval we effect a multifractal formalism, i.e., decompose the phase space into...

ONE-DIMENSIONAL MAPS | DIFFEOMORPHISMS | MATHEMATICS | MATHEMATICS, APPLIED | AVERAGES | CONFORMAL EXPANDING MAPS | CONTINUOUS INVARIANT-MEASURES | HYPERBOLICITY | S-UNIMODAL MAPS | SYSTEMS | POINTS | LARGE DEVIATIONS | Probability | Quadratic programming | Fractals | Towers | Maps | Decomposition | Entropy | Deviation | Formalism | Dynamical systems | Invariants | Mathematics - Dynamical Systems

ONE-DIMENSIONAL MAPS | DIFFEOMORPHISMS | MATHEMATICS | MATHEMATICS, APPLIED | AVERAGES | CONFORMAL EXPANDING MAPS | CONTINUOUS INVARIANT-MEASURES | HYPERBOLICITY | S-UNIMODAL MAPS | SYSTEMS | POINTS | LARGE DEVIATIONS | Probability | Quadratic programming | Fractals | Towers | Maps | Decomposition | Entropy | Deviation | Formalism | Dynamical systems | Invariants | Mathematics - Dynamical Systems

Journal Article

Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 01/2017, Volume 34, Issue 1, pp. 31 - 43

We explicitly determine the spectrum of transfer operators (acting on spaces of holomorphic functions) associated to analytic expanding circle maps arising...

Spectrum of transfer operators | Expanding maps | Blaschke products | Adjoint operators | Mixing rates | Analytic circle maps | MATHEMATICS, APPLIED

Spectrum of transfer operators | Expanding maps | Blaschke products | Adjoint operators | Mixing rates | Analytic circle maps | MATHEMATICS, APPLIED

Journal Article

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