58 citations · 210 across the 15 of their papers we have counts for
16 papers · 1 filter
Continuum-wise hyperbolicity is exactly the pseudo-Anosov dynamics with spine singularities
Rodrigo Arruda, Bernardo Carvalho, Piotr Oprocha +1
We establish a complete structural classification for cw-hyperbolic surface homeomorphisms. Specifically, we prove that a surface homeomorphism is cw-hyperbolic if, and onl…
-generic continuum-wise expansive surface diffeomorphisms
Alfonso Artigue, Bernardo Carvalho, José Cueto
We exhibit a local residual set of surface diffeomorphisms that are continuum-wise expansive but are not expansive. We also exhibit an open and dense set of surface dif…
Box dimension of stable sub-slices of fractal graphs over Anosov automorphisms
Bernardo Carvalho, Rafael da Costa Pereira
We consider fractal graphs invariant by a skew product of the form where ,…
Stable/unstable holonomies, density of periodic points, and transitivity for continuum-wise hyperbolic homeomorphisms
Bernardo Carvalho, Elias Rego
We discuss different regularities on stable/unstable holonomies of cw-hyperbolic homeomorphisms and prove that if a cw-hyperbolic homeomorphism has continuous joint stable/unstable…
Continuum-wise hyperbolic homeomorphisms on surfaces
Rodrigo Arruda, Bernardo Carvalho, Alberto Sarmiento
This paper discusses the dynamics of continuum-wise hyperbolic surface homeomorphisms. We prove that -hyperbolic surface homeomorphisms containing only a finite set of spines…
First-time sensitive homeomorphisms
Mayara Antunes, Bernardo Carvalho
We introduce first-time sensitivity for a homeomorphism of a compact metric space, that is a condition on the first increasing times of open balls of the space. Continuum-wise expa…
Sensitivity, local stable/unstable sets and shadowing
Mayara Antunes, Bernardo Carvalho, Margoth Tacuri
In this paper we study local stable/unstable sets of sensitive homeomorphisms with the shadowing property defined on compact metric spaces. We prove that local stable/unstable sets…
Continuum-wise hyperbolicity
Alfonso Artigue, Bernardo Carvalho, Welington Cordeiro +1
We introduce continuum-wise hyperbolicity, a generalization of hyperbolicity with respect to the continuum theory. We discuss similarities and differences between topological hyper…
Suspensions of homeomorphisms with the two-sided limit shadowing property
Jesús Aponte, Bernardo Carvalho, Welington Cordeiro
In this paper we discuss the two-sided limit shadowing property for continuous flows defined in compact metric spaces. We analyze some of the results known for the case of homeomor…
Countably and entropy expansive homeomorphisms with the shadowing property
Alfonso Artigue, Bernardo Carvalho, Welington Cordeiro +1
We discuss the dynamics beyond topological hyperbolicity considering homeomorphisms satisfying the shadowing property and generalizations of expansivity. It is proved that transiti…
Beyond topological hyperbolicity: the L-shadowing property
A. Artigue, B. Carvalho, W. Cordeiro +1
In this paper we further explore the L-shadowing property defined in [17] for dynamical systems on compact spaces. We prove that structurally stable diffeomorphisms and some pseudo…
Positively n-expansive homeomorphisms and the L-shadowing property
Bernardo Carvalho, Welington Cordeiro
We discuss further the dynamics of n-expansive homeomorphisms with the shadowing property, started in [7]. The L-shadowing property is defined and the dynamics of n-expansive homeo…
N-expansive homeomorphisms with the shadowing property
Bernardo Carvalho, Welington Cordeiro
We discuss the dynamics of -expansive homeomorphisms with the shadowing property defined on compact metric spaces. For every , we exhibit an -expansive homeom…
Product Anosov diffeomorphisms and the two-sided limit shadowing property
Bernardo Carvalho
We characterize product Anosov diffeomorphisms in terms of the two-sided limit shadowing property. It is proved that an Anosov diffeomorphism is a product Anosov diffeomorphism if…
On homeomorphisms with the two-sided limit shadowing property
Bernardo Carvalho, Dominik Kwietniak
We prove that the two-sided limit shadowing property is among the strongest known notions of pseudo-orbit tracing. It implies shadowing, average shadowing, asymptotic average shado…
Hyperbolicity, transitivity and the two-sided limit shadowing property
Bernardo Carvalho
We explore the notion of two-sided limit shadowing property introduced by Pilyugin \cite{P1}. Indeed, we characterize the -interior of the set of diffeomorphisms with such a p…