arXiv subjects

Jana Rodriguez Hertz

Publications and source records attributed to Jana Rodriguez Hertz.

21 records · Page 2Linked to original sources

arXiv2004

Continuum-wise expansive homeomorphisms on Peano continua

On a Peano continuum, all local stable and unstable components of a continuum-wise expansive homeomorphism are non trivial. In particular, there is sensitive dependence on initial conditions. This generalizes results in \cite{h,l} about lack of Lyapunov stable points (weak sinks) and existence of non trivial stable and unstable components for expansive homeomorphisms on Peano continua. We also use this fact to generalize a result in \cite{ktt}: a Peano curve $X$ admitting a continuum-wise expansive homeomorphism is nowhere rim-countable. However, it is not resolved the question of whether such a dynamics could be possible in a locally planar Peano curve. Some other questions are posed.

math.DS↗

arXiv2002

There are no stable points for continuum-wise expansive homeomorphisms

We obtain some results about continuum-wise expansive homeomorphisms, such as non-existence of stable points and presence of non-trivial connected components within the local stable and unstable sets. These facts have been of importance in theorems of classification of expansive homeomorphisms. They are achieved now, however, by new and self contained techniques that hold on more general settings.

math.DS↗

arXiv2001

On manifolds supporting quasi Anosov diffeomorphisms

Let $M$ be an $n$-dimensional manifold supporting a quasi Anosov diffeomorphism. If $n=3$ then either $M={\mathbb T}^3$, in which case the diffeomorphisms is Anosov, or else its fundamental group contains a copy of ${\mathbb Z} ^6$. If $n=4$ then $Π_1(M)$ contains a copy of ${\mathbb Z} ^4$, provided that the diffeomorphism is not Anosov.

math.DS↗