arXiv subjects

Victor Janeiro

Publications and source records attributed to Victor Janeiro.

2 recordsLinked to original sources

arXiv2026

Inverse SRB measures for endomorphisms on surfaces

We extend D. Burguet's construction of SRB measures for the non-invertible scenario obtaining hyperbolic invariant measures with absolutely continuous disintegrations on stable manifolds for a certain class of endomorphisms on the two-torus. The constructed measures also maximize the folding entropy, and we call them equidistributed inverse SRB measures. For dissipative perturbations of the examples given by M. Andersson, P. Carrasco and R. Saghin we obtain existence, uniqueness and continuity with respect to the map of the equidistributed inverse SRB measures as well as the SPR property of the stable geometric potential for such maps.

math.DS↗

arXiv2023

Existence of robust non-uniformly hyperbolic endomorphism in homotopy classes

We extend the results of arXiv:2206.08295v2 by showing that any homothety in $\mathbb T^2$ is homotopic to a non-uniformly hyperbolic ergodic area preserving map, provided that its degree is at least $5^2$. We also address other small topological degree cases not considered in the previous article. This proves the existence of a $\mathcal C^1$ open set of non-uniformly hyperbolic systems, that intersects essentially every homotopy classes in $\mathbb T^2$, where the Lyapunov exponents vary continuously.

math.DS↗