arXiv subjects

Catalina Freijo

Publications and source records attributed to Catalina Freijo.

6 recordsLinked to original sources

arXiv2025

Rotation sets for random compositions of $\T$ homeomorphisms

We study cocycles of homeomorphisms of $\T$ in the isotopy class of the identity over shift spaces, using as a tool a novel definition of rotation sets inspired in the classical work of Miziurewicz and Zieman. We discuss different notions of rotation sets, for the full cocyle as well as for measures invariant by the shift dynamics on the base. We present some initial results on the shape of rotation sets, continuity of rotation sets for shift-invariant measures, and bounded displacements for irrotational cocyles, as well as a few interesting examples in an attempt to motive the development of the topic.

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arXiv2025

Cohomology of Lipschitz-valued cocycles

We consider the set of H\"older continuous cocycles over a finite shift acting on a group of Lipschitz homeomorphisms Lip(G), where G is a metrisable compact topological group. We establish that two dominated cocycles that coincide over periodic points of the base are cohomologous, with the conjugacy being H\"older continuous. Moreover, we prove that, under an additional condition, the existence of a measurable conjugacy implies the existence of a H\"older continuous conjugacy between the cocycles.

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arXiv2022

Continuity of Lyapunov exponents for non-uniformly fiber-bunched cocycles

We provide conditions which imply the continuity of the Lyapunov exponents for non-uniformly fiber-bunched cocycles in $SL(2,\mathbb{R})$. The main theorem is an extension of the result of Backes, Brown and Butler and gives a partial answer to a conjecture of Marcelo Viana.

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arXiv2022

Continuity of the Lyapunov exponents of non-invertible random cocycles with constant rank

In this paper we establish uniform large deviations estimates of exponential type and Hölder continuity of the Lyapunov exponents for random non-invertible cocycles with constant rank.

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arXiv2022

A dynamical Thouless formula

In this paper we establish an abstract, dynamical Thouless-type formula for affine families of $\mathrm{GL} (2,\mathbb{R})$ cocycles. This result extends the classical formula relating, via the Hilbert transform, the maximal Lyapunov exponent and the integrated density of states of a Schrödinger operator. Here, the role of the integrated density of states will be played by a more geometrical quantity, the fibered rotation number. As an application of this formula we present limitations on the modulus of continuity of random linear cocycles. Moreover, we derive Hölder-type continuity properties of the fibered rotation number for linear cocycles over various base dynamics.

math.DS↗

arXiv2022

Density of non-zero exponent of contraction for pinching cocycles on Hom(S^1)

We consider pinching cocycles taking values in the space of homeomorphisms of the circle over an hyperbolic base. Using the Invariance Principle of Malicet, we prove that the cocycles having non-zero exponents of contraction are dense. In this article we generalize some common notions an results known of linear cocycles and cocycles of diffeomorphisms, to the non-linear non-differentiable case.

math.DS↗