In this paper we study the relationship between the strict locally minimizing orbits for time dependent lagrangian systems and hyperbolicity properties of the corresponding lagrangian flow.
In this paper we investigate the Margulis-Ruelle inequality for general Riemannian manifolds (possibly noncompact and with boundary) and show that it always holds under integrable condition.
We study various compactifications of moduli space of Newton maps. Mainly, we focus on GIT compactifiaction and Deligne-Mumford compactification. Then we explore the relations among these compactifications.
We show in this paper a sufficient condition for the existence of solution, the synchronized and the periodic locked state in abstract mean field models.
We prove that restricted to the subset of fiber-bunched elements of the space of $GL(2,\mathbb{R})$-valued cocycles Oseledets subspaces vary continuously, in measure, with respect to the cocycle.
Let $M$ be a triangulable compact manifold. We prove that, among closed subgroups of $\homeo_{0}(M)$ (the identity component of the group of homeomorphisms of $M$), the subgroup consisting of volume preserving elements is maximal.
We prove that the Julia set of a rational function $f$ is computable in polynomial time, assuming that the postcritical set of $f$ does not contain any critical points or parabolic periodic orbits.
It is shown that if $E$ is any subset of $\Bbb N$ such that either $1\in E$ or $2\in E$ then there is a mixing transformation whose set of spectral multiplicities is $E$.
We prove a spectral decomposition theorem for a well-known self-similar graph, for some finite graphs which are quotients of this graph and for a compactification of it.
We give a new proof of the Cobham's first theorem using ideas from symbolic dynamics and of the Cobham-Semenov theorem (in the primitive case) using ideas from tiling dynamics.