A natural occurrence of shift equivalence
A natural occcurrence of shift equivalence in a purely algebraic setting is exhibited.
A non-linear discrete-time dynamical system related to epidemic SISI model
We consider SISI epidemic model with discrete-time. The crucial point of this model is that an individual can be infected twice. This non-linear evolution operator depends on seven parameters and we assume that the population size under consideration is constant, so death rate is the same with birth rate per unit time. Reducing to quadratic stochastic operator (QSO) we study the dynamical system of the SISI model.
A topological characterization of holomorphic parabolic germs in the plane
J.-M. Gambaudo and É. Pécou introduced the "linking property" in the study of the dynamics of germs of planar homeomorphisms in order to provide a new proof of Naishul's theorem. In this paper we prove that the negation of the Gambaudo-Pécou property characterizes the topological dynamics of holomorphic parabolic germs. As a consequence, a rotation set for germs of surface homeomorphisms around a fixed point can be defined, and it turns out to be non-trivial except for countably many conjugacy classes....
Asymptotic period in dynamical systems in metric spaces
We introduce the notions of asymptotic period and asymptotically periodic orbits in metric spaces. We study some properties of these notions and their connections with ω-limit sets. We also discuss the notion of growth rate of such orbits and describe its properties in an extreme case.
Attracting dynamics of exponential maps.