Topological pressure for discontinuous semiflows and a variational principle for impulsive dynamical systems

We introduce four, a priori different, notions of topological pressure for possibly discontinuous semiflows acting on compact metric spaces and observe that they all agree with the classical one when restricted to the continuous setting. Moreover, for a class of \emph{impulsive semiflows}, which are examples of discontinuous systems, we prove a variational principle. As a consequence, we conclude that for this class of systems the four notions coincide and, moreover, they also coincide with the notion of topological pressure introduced in \cite{ACS17}

Mean Dimension and Metric Mean Dimension for Non-autonomous Dynamical Systems

In this paper we extend the definitions of mean dimension and metric mean dimension for non-autonomous dynamical systems. We show some properties of this extension and furthermore some applications to the mean dimension and metric mean dimension of single continuous maps

Extreme Value Laws for dynamical systems with countable extremal sets

We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of the process, which is related to the entrance in certain regions of the phase space, which correspond to neighbourhoods of the maximal set $\mathcal M$, i.e. the set of points where the observable is maximised. The main novelty here is the fact that we consider that the set $\mathcal M$ may have a countable number of points, which are associated by belonging to the orbit of a certain point, and may have accumulation points. In order to prove the existence of distributional limits and study the intensity of clustering, given by the Extremal Index, we generalise the conditions previously introduced in \cite{FFT12,FFT15}.Comment: arXiv admin note: text overlap with arXiv:1505.0155

Topological and metric emergence of continuous maps

We prove that the homeomorphisms of a compact manifold with dimension one have zero topological emergence, whereas in dimension greater than one the topological emergence of a C^0-generic conservative homeomorphism is maximal, equal to the dimension of the manifold. Moreover, we show that the metric emergence of continuous self-maps on compact metric spaces has the intermediate value property