23 citations · 39 across the 9 of their papers we have counts for
11 papers
Infinite-Piecewise Expanding Maps: Chaos, Ergodicity and Invariant-Set Complexity
Matheus G. C. Cunha, Douglas D. Novaes, Gabriel Ponce
In this paper, we study a class of one-dimensional piecewise maps defined by infinitely many smooth expanding branches. This class arises naturally in the context of non-smooth dyn…
On the Hausdorff dimension and Cantor set structure of sliding Shilnikov invariant sets
Matheus G. C. Cunha, Douglas D. Novaes, Gabriel Ponce
The concept of sliding Shilnikov connection has been recently introduced and represents an important notion in Filippov systems, because its existence implies chaotic behavior on a…
Ergodic properties of partially hyperbolic diffeomorphisms with topological neutral center
Gabriel Ponce
In this work we obtain some metric and ergodic properties of partially hyperbolic diffeomorphisms with one-dimensional topological neutral center, mainly regarding the beh…
Unstable entropy of partially hyperbolic diffeomorphisms along non-compact subsets
Gabriel Ponce
Given a partially hyperbolic diffeomorphism defined on a compact Riemannian manifold , in this paper we define the concept of unstable topological entropy of…
Measure Rigidity and Disintegration: Time-one map of flows
Gabriel Ponce, Régis Varão
An invariant measure for a flow is, of course, an invariant measure for any of its time-t maps. But the converse is far from being true. Hence, one may naturally ask: What is the o…
Chaos induced by sliding phenomena in Filippov systems
Douglas Duarte Novaes, Gabriel Ponce, Régis Varão
In this paper we provide a full topological and ergodic description of the dynamics of Filippov systems nearby a sliding Shilnikov orbit. More specifically we prove that the first…