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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
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
Journal Article
Journal of Statistical Physics, ISSN 0022-4715, 1/2017, Volume 166, Issue 1, pp. 114 - 136
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
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
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 inf⁡f′>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
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
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
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
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
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
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
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
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
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
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 4/2017, Volume 351, Issue 2, pp. 775 - 835
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
Journal Article
Nonlinearity, ISSN 0951-7715, 02/2015, Volume 28, Issue 2, pp. 407 - 434
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
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
Journal Article
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