26 citations · 151 across the 27 of their papers we have counts for
32 papers
Pointwise Hölder continuity of Lyapunov exponents of random matrix products
Pablo G. Barrientos
We prove that if the first Lyapunov exponent of a compactly supported random matrix product is simple, then it is pointwise Hölder continuous for the Wasserstein--Hausdorff distanc…
Limit theorems for random matrix products with a simple top Lyapunov exponent
Pablo G. Barrientos, Dominique Malicet
We study products of independent, identically distributed random matrices with an exponential moment and a simple top Lyapunov exponent, without assuming irreducibility. Outside an…
(co)Quasi-irreducible and (co)expanding random maps
Pablo G. Barrientos, Isaia Nisoli, Dominique Malicet
We study quasi-irreducibility, expansion, and their cotangent duals for random (local) diffeomorphisms on compact invariant sets of a Riemannian manifold. Quasi-irreducibilit…
Integral representation of Lyapunov exponents
Pablo G. Barrientos, Isaia Nisoli
We introduce a new operator-theoretic construction of Lyapunov growth for Markov-driven systems. The construction is based on an abstract variational principle for asymptotic growt…
Robust heterodimensional cycles of co-index two via split blending machines
Pablo G. Barrientos, Lorenzo J. Díaz, Yuri Ki +2
We consider diffeomorphisms with heterodimensional cycles of co-index two, associated with saddles and having unstable indices and , respectively. In a p…
Finitude of physical measures for Markovian random maps
Pablo G. Barrientos, Dominique Malicet, Fumihiko Nakamura +2
We study the finiteness of physical measures for skew-product transformations associated with discrete-time random dynamical systems driven by ergodic Markov chains. We develop…
Historical behavior of skew products and arcsine laws
Pablo G. Barrientos, Raul R. Chavez
We study the occurrence of historical behavior for almost every point in the setting of skew products with one-dimensional fiber dynamics. Under suitable ergodic conditions, we est…
Mostly contracting random maps
Pablo G. Barrientos, Dominique Malicet
We study the long-term behavior of independent random iterations of Lipschitz transformations on a compact metric space. Such a random map is said to be mostly contracting if all L…
Zero Lyapunov Exponents in Transitive Skew-products of Iterated Function Systems
Pablo G. Barrientos, Joel Angel Cisneros
We study the class of transitive skew-products associated with iterated function systems of circle diffeomorphisms. We can approximate any transitive skew-product by maps in this c…
Minimal Strong Foliations in Skew-products of Iterated Function Systems
Pablo G. Barrientos, Joel Angel Cisneros
We study locally constant skew-product maps over full shifts of finite symbols with arbitrary compact metric spaces as fiber spaces. We introduce a new criterion to determine the d…
Finitude of physical measures for random maps
Pablo G. Barrientos, Fumihiko Nakamura, Yushi Nakano +1
For random compositions of independent and identically distributed measurable maps on a Polish space, we study the existence and finitude of absolutely continuous ergodic stationar…
Homoclinic tangencies leading to robust heterodimensional cycles
Pablo G. Barrientos, Lorenzo J. Díaz, Sebastián A. Pérez
We consider () diffeomorphisms defined on manifolds of dimension with homoclinic tangencies associated to saddles. Under generic properties, w…
Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, II: Applications
Sébastien Alvarez, Pablo G. Barrientos, Dmitry Filimonov +4
In the first part of this work we have established an efficient method to obtain a topological classification of locally discrete, finitely generated, virtually free subgroups of r…
Historic wandering domains near cycles
Pablo G. Barrientos
We explain how to obtain non-trivial historic contractive wandering domains for a dense set of diffeomorphisms in certain type of -Newhouse domains of homoclinic tangencies in…
Topological entropy and Hausdorff dimension of irregular sets for non-hyperbolic dynamical systems
Pablo G. Barrientos, Yushi Nakano, Artem Raibekas +1
We systematically investigate examples of non-hyperbolic dynamical systems having irregular sets of full topological entropy and full Hausdorff dimension. The examples include some…
Berger domains and Kolmogorov typicality of infinitely many invariant circles
Pablo G. Barrientos, Artem Raibekas
Using the novel notion of parablender, P. Berger proved that the existence of finitely many attractors is not Kolmogorov typical in parametric families of diffeomorphisms. Here, mo…
Typical coexistence of infinitely many strange attractors
Pablo G. Barrientos, Juan David Rojas
We prove that the coexistence of infinitely many prevalent Hénon-like phenomena is Kolmogorov typical in sectional dissipative -Berger domains of parameter families of dif…
Robust degenerate unfoldings of cycles and tangencies
Pablo G. Barrientos, Artem Raibekas
We construct open sets of degenerate unfoldings of heterodimensional cycles of any co-index and homoclinic tangencies of arbitrary codimension . These sets are known to…
Historic behavior in non-hyperbolic homoclinic classes
Pablo G. Barrientos, Shin Kiriki, Yushi Nakano +2
We show that -generically for diffeomorphisms of manifolds of dimension , a homoclinic class containing saddles of different indices has a residual subset where the or…
Robust Heteroclinic Tangencies
Pablo G. Barrientos, Sebastián A. Pérez
We construct diffeomorphisms in dimension exhibiting -robust heteroclinic tangencies.
Ergodicity of non-autonomous discrete systems with non-uniform expansion
Pablo G. Barrientos, Abbas Fakhari
We study the ergodicity of non-autonomous discrete dynamical systems with non-uniform expansion. As an application we get that any uniformly expanding finitely generated semigroup…
Chaos near a reversible homoclinic bifocus
Pablo G. Barrientos, Artem Raibekas, Alexandre A. P. Rodrigues
We show that any neighborhood of a non-degenerate reversible bifocal homoclinic orbit contains chaotic suspended invariant sets on -symbols for all . This will be achie…
Extremal exponents of random products of conservative diffeomorphisms
Pablo G. Barrientos, Dominique Malicet
We show that for a -open and -dense subset of the set of ergodic iterated function systems of conservative diffeomorphisms of a finite-volume manifold of dimension $d\g…
Robustly non-hyperbolic transitive symplectic dynamics
Pablo G. Barrientos, Artem Raibekas
We construct symplectomorphisms in dimension having a semi-local robustly transitive partially hyperbolic set containing -robust homoclinic tangencies of any codimen…