37 citations · 135 across the 30 of their papers we have counts for
30 papers
Entropy formula for C1 expanding maps
Eleonora Catsigeras, Fernando Valenzuela Gómez
We prove that the (necessarily existing) pseudo-physical or SRB-like measures of C1 expanding dynamical systems on a compact Riemannian manifold satisfy Pesin entropy formula. We i…
A spectral decomposition of the attractor of piecewise contracting maps of the interval
A. Calderón, E. Catsigeras, P. Guiraud
We study the asymptotic dynamics of piecewise contracting maps defined on a compact interval. For maps that are not necessarily injective, but have a finite number of local extrema…
Ergodic measures with infinite entropy
Eleonora Catsigeras, Serge Troubetzkoy
We construct ergodic probability measures with infinite metric entropy for typical continuous maps and homeomorphisms on compact manifolds. We also construct sequences of such meas…
Invariant measures for typical continuous maps on manifolds
Eleonora Catsigeras, Serge Troubetzkoy
We study the invariant measures of typical maps on compact connected manifolds with or without boundary, and also of typical homeomorphisms. We prove that the weak closur…
Ergodic Theorems for the Transfer Operators of Noisy Dynamical Systems
Eleonora Catsigeras
We consider stationary stochastic dynamical systems evolving on a compact metric space, by perturbing a deterministic dynamics with a random noise, added according to an arbitrary…
Empiric stochastic stability of physical and pseudo-physical measures
Eleonora Catsigeras
We define the empiric stochastic stability of an invariant measure in the finite-time scenario, the classical definition of stochastic stability. We prove that an invariant measure…
Pseudo-physical measures for typical continuous maps of the interval
Eleonora Catsigeras, Serge Troubetzkoy
We study the measure theoretic properties of typical C 0 maps of the interval. We prove that any ergodic measure is pseudo-physical, and conversely, any pseudo-physical measure is…
Complexity of injective piecewise contracting interval maps
Eleneora Catsigeras, Pierre Guiraud, Arnaud Meyroneinc
We study the complexity of the itineraries of injective piecewise contracting maps on the interval. We prove that for any such map the complexity function of any itinerary is event…
Weak Pseudo-Physical Measures and Pesin's Entropy Formula for Anosov C1 diffeomorphisms
Eleonora Catsigeras, Marcelo Cerminara, Heber Enrich
We consider C1 Anosov diffeomorphisms on a compact Riemannian manifold. We define the weak pseudo-physical measures, which include the physical measures when these latter exist. We…
Topological Entropy on Points without Physical-like Behaviour
Eleonora Catsigeras, Xueting Tian, Edson Vargas
We study a class of asymptotically entropy-expansive diffeomorphisms with dominated splitting on a compact manifold , that satisfy the specification property. This class i…
Oscillating statistics of transitive dynamics
Eleonora Catsigeras
We prove that topologically generic orbits of C0 transitive and non-uniquely ergodic dynamical systems, exhibit an extremely oscillating asymptotical statistics. Precisely, the min…
Dominated Splitting, Partial Hyperbolicity and Positive Entropy
Eleonora Catsigeras, Xueting Tian
Let be a diffeomorphism with a dominated splitting on a compact Riemanian manifold without boundary. We state and prove several sufficient conditions f…
Coalitions of pulse-interacting dynamical units
Eleonora Catsigeras
We prove that large global systems of interacting (non necessarily similar) dynamical units that are coupled by cooperative impulses, recurrently exhibit the so called grand coalit…
Dale's Principle is necessary for an optimal neuronal network's dynamics
Eleonora Catsigeras
We study a mathematical model of biological neuronal networks composed by any finite number of non necessarily identical cells. The model is a deterministic dynamical sy…
Teoría Ergódica de los Atractores Topológicos y Estadísticos (Ergodic Theory of Topological and Statistical Attractors) (Spanish)
Eleonora Catsigeras
This is a textbook, in Spanish, for an introductory short course that focusses on the ergodic properties of topological and statistical attractors. It is directed to graduate stude…
Dynamics of large cooperative pulsed-coupled networks
Eleonora Catsigeras
We study the deterministic dynamics of networks N composed by m non identical, mutually pulse-coupled cells. We assume weighted, asymmetric and positive (cooperative) interactions…
Pesin Entropy Formula for C1 Diffeomorphisms with Dominated Splitting
Eleonora Catsigeras, Marcelo Cerminara, Heber Enrich
For any C1 diffeomorphism with dominated splitting we consider a nonempty set of invariant measures which describes the asymptotic statistics of Lebesgue-almost all orbits. They ar…
Equilibrium States and SRB-like measures of C1 Expanding Maps of the Circle
Eleonora Catsigeras, Heber Enrich
For any C1 expanding map f of the circle we study the equilibrium states for the potential -log |f'|. We formulate a C1 generalization of Pesin's Entropy Formula that holds for all…
Observable Optimal State Points of Sub-additive Potentials
Eleonora Catsigeras, Yun Zhao
For a sequence of sub-additive potentials, Dai [Optimal state points of the sub-additive ergodic theorem, Nonlinearity, 24 (2011), 1565-1573] gave a method of choosing state points…
On the Asymptotic Properties of Piecewise Contracting Maps
E. Catsigeras, P. Guiraud, A. Meyroneinc +1
We study the asymptotic dynamics of maps which are piecewise contracting on a compact space. These maps are Lipschitz continuous, with Lipschitz constant smaller than one, when res…
SRB-like measures for C0 dynamics
Eleonora Catsigeras, Heber Enrich
For any continuous map f on a compact manifold M, we define the SRB-like (or observable) probabilities as a generalization of Sinai-Ruelle-Bowen (i.e. physical) measures. We prove…
Deterministic Dynamics and Chaos: Epistemology and Interdisciplinary Methodology
Eleonora Catsigeras
We analyze, from a theoretical viewpoint, the bidirectional interdisciplinary relation between mathematics and psychology, focused on the mathematical theory of deterministic dynam…
Chaos and stability in a model of inhibitory neuronal network
Eleonora Catsigeras
We analyze the dynamics of a deterministic model of inhibitory neuronal networks proving that the discontinuities of the Poincare map produce a never empty chaotic set, while its c…
On Ilyashenko's Statistical Attractors
Eleonora Catsigeras
We define a minimal alpha-observability of Ilyashenko's statistical attractors. We prove that the space is always full Lebesgue decomposable into pairwise disjoint sets that are Le…