This paper is concerned with the study of fuzzy dynamical systems. Let (XM ) be a fuzzy metric space in the sense of George and Veeramani. A fuzzy discrete dynamical system is given by any fuzzy continuous self-map dened on X. We introduce the various fuzzy shad- owing and fuzzy topological transitivity on a fuzzy discrete dynamical systems. Some relations between this notions have been proved.

Recently, dynamical phase transitions have been identified based on the nonanalytic behavior of the Loschmidt echo in the thermodynamic limit [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)]. By introducing conditional probability amplitudes, we show how dynamical phase transitions can be further classified, both mathematically, and potentially in experiment. This leads to the definition of f...

We present a topological technique for analyzing dynamical systems with complex behavior, based on the general notion of covering relations. Our method can be used to study multidimensional dynamical systems with an arbitrary number of ‘topologically’ expanding directions.

The aim of this paper is to present and analyze a minimal chaotic map of the plane, then we describe in detail the dynamical behavior of this map, along with some other dynamical phenomena.