activity
20122026
most citedSymbolic blender-horseshoes and applications

26 citations · 151 across the 27 of their papers we have counts for

collaborators

32 papers

math.DS2026

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…

math.DS2026

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…

math.DS2026

(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…

math.DS2026

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…

math.DS2025

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…

math.DS2025

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…

math.DS2025

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…

math.DS2024

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…

math.DS2024

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…

math.DS2023★ 1 cited

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…

math.DS2022★ 1 cited

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…

math.DS2021

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…

math.DS2021

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…

math.DS2021★ 5 cited

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…

math.DS2021★ 3 cited

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…

math.DS2021★ 1 cited

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…

math.DS2021

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…

math.DS2019★ 6 cited

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…

math.DS2019★ 20 cited

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…

math.DS2019

Robust Heteroclinic Tangencies

Pablo G. Barrientos, Sebastián A. Pérez

We construct diffeomorphisms in dimension exhibiting -robust heteroclinic tangencies.

math.DS2018

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…

math.DS2018★ 6 cited

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…

math.DS2018★ 4 cited

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…

math.DS2017

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…