26 citations · 114 across the 12 of their papers we have counts for
11 papers · 1 filter
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…
Statistical determinism in non-Lipschitz dynamical systems
Theodore D. Drivas, Alexei A. Mailybaev, Artem Raibekas
We study a class of ordinary differential equations with a non-Lipschitz point singularity, which admit non-unique solutions through this point. As a selection criterion, we introd…
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…
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…
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…
Robust tangencies of large codimension
Pablo G. Barrientos, Artem Raibekas
We construct -robust homoclinic and heterodimensional tangencies of large codimension inside transitive partially hyperbolic sets.
Robust cycles and tangencies of large codimension
Pablo G. Barrientos, Artem Raibekas
We construct partially hyperbolic diffeomorphisms having semi-local robustly transitive sets with -robust cycles of any co-index. These constructions also provide a new method…
Dynamics of iterated function systems on the circle close to rotations
Pablo G. Barrientos, Artem Raibekas
We study the dynamics of iteration function systems generated by a pair of circle diffeomorphisms close to rotations in the -topology. We characterize the obstru…
Symbolic blender-horseshoes and applications
Pablo G. Barrientos, Yuri Ki, Artem Raibekas
We study partially-hyperbolic skew-product maps over the Bernoulli shift with Hölder dependence on the base points. In the case of contracting fiber maps, symbolic blender-horsesho…