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We obtain the complete conjugacy invariants of expansive Lorenz maps and for any given two expansive Lorenz maps, there are two unique sequences of $(beta_{i},alpha_{i})$ pairs. In this way, we can define the classification of expansive Lorenz maps. Moreover, we investigate the uniform linearization of expansive Lorenz maps through periodic renormalization.
We prove that a homeomorphism of a compact metric space has an expansive measure cite{ms} if and only if it has many ones with invariant support. We also study homeomorphisms for which the expansive measures are dense in the space of Borel probabilit
We study homeomorphisms of compact metric spaces whose restriction to the nonwandering set has the pseudo-orbit tracing property. We prove that if there are positively expansive measures, then the topological entropy is positive. Some short applications of this result are included.
We shall show that the rotation of some irrational rotation number on the circle admits suspensions which are kinematic expansive.
We study directional mean dimension of $mathbb{Z}^k$-actions (where $k$ is a positive integer). On the one hand, we show that there is a $mathbb{Z}^2$-action whose directional mean dimension (considered as a $[0,+infty]$-valued function on the torus)
This paper presents algebraic methods for the study of polynomial relative invariants, when the group G formed by the symmetries and relative symmetries is a compact Lie group. We deal with the case when the subgroup H of symmetries is normal in G wi