8 papers
(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…
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…
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. DÃaz, 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…
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…