Related papers: Sub-additive unstable topological pressure on satu…
We study $C^1$-robustly transitive and nonhyperbolic diffeomorphisms having a partially hyperbolic splitting with one-dimensional central bundle whose strong un-/stable foliations are both minimal. {In dimension $3$, an important class of…
Let $(X,d,f)$ be a dynamical system, where $(X,d)$ is a compact metric space and $f:X\rightarrow X$ is a continuous map. Using the concepts of \textit{g-almost product property} and \textit{uniform separation property} introduced by Pfister…
We consider partially hyperbolic diffeomorphisms on compact manifolds where the unstable and stable foliations stably carry some unique non-trivial homologies. We prove the following two results: if the center foliation is one dimensional,…
We study two variations of Bowen's definitions of topological entropy based on separated and spanning sets which can be applied to the study of discontinuous semiflows on compact metric spaces. We prove that these definitions reduce to…
For a $C^{r}$ $(r>1)$ diffeomorphism on a compact manifold that admits a dominated splitting, this paper establishes the upper semi-continuity of the entropy map. More precisely, this paper establishes the upper semi-continuity of the…
Given a non-conformal repeller $\Lambda$ of a $C^{1+\gamma}$ map, we study the Hausdorff dimension of the repeller and continuity of the sub-additive topological pressure for the sub-additive singular valued potentials. Such a potential…
Let $f$ be a $C^2$ diffeomorphism on a compact manifold. Ledrappier and Young introduced entropies along unstable foliations for an ergodic measure $\mu$. We relate those entropies to covering numbers in order to give a new upper bound on…
In arXiv:1801.01238 a variation of Bowen's topological entropy that can be applied to the study of discontinuous semiflows on compact metric spaces was introduced. The main novetly is the use of certain family of pseudosemimetrics…
We study the $C^1$-topological properties of the subset of non-uniform hyperbolic diffeomorphisms in a certain class of $C^2$ partially hyperbolic symplectic systems which have bounded $C^2$ distance to the identity. In this set, we prove…
Climenhaga showed the applicability of Bowen equation to arbitrary subset of a compact metric space. The main purpose of this paper is to generalize the main result of Climenhaga to free semigroup actions for non-compact sets. We introduce…
We prove three formulas for computing topological pressure of $C^1$-generic conservative diffeomorphism and show the continuity of topological pressure with respect to these diffeomorphisms. We prove for these generic diffeomorphisms that…
In this article we prove estimates for the topological pressure of the set of points whose Birkhoff time averages are far from the space averages corresponding to the unique equilibrium state that has a weak Gibbs property. In particular,…
This article is devoted to the investigation of the topological pressure of generic points for nonuniformly hyperbolic systems via Pesin theory. In particular, our result can be applied to the nonuniformly hyperbolic diffeomorphisms…
We study several notions of topological pressure and capacities for multi-potentials $\Phi \in \mathcal C(X;\mathbb R)^m$, with respect to finitely generated continuous semigroups $G$ on a compact metric space $X$. We introduce the…
We study a class of asymptotically entropy-expansive $C^1$ diffeomorphisms with dominated splitting on a compact manifold $M$, that satisfy the specification property. This class includes, in particular, transitive Anosov diffeomorphisms…
Without any additional conditions on subadditive potentials, this paper defines subadditive measure-theoretic pressure, and shows that the subadditive measure-theoretic pressure for ergodic measures can be described in terms of…
Using methods from symplectic topology, we prove existence of invariant variational measures associated to the flow $\phi_H$ of a Hamiltonian $H\in C^{\infty}(M)$ on a symplectic manifold $(M,\omega)$. These measures coincide with Mather…
This paper introduces the concept of average conformal hyperbolic sets, which admit only one positive and one negative Lyapunov exponents for any ergodic measure. For an average conformal hyperbolic set of a C1 diffeomorphism, utilizing the…
The (measure-theoretical) entropy of a diffeomorphism along an expanding invariant foliation is the rate of complexity generated by the diffeomorphism along the leaves of the foliation. We prove that this number varies upper…
For dynamical systems with infinite topological entropy, the classical entropy fails to quantify their complexity effectively, while the metric mean dimension provides a natural extension in this context. In this paper, we study the…