For linear dynamical systems (in continuous-time and discrete-time), we revisit extend the concepts of hypocoercivity hypocontractivity give a detailed analysis relations these to (asymptotic) stability, as well (semi-)dissipativity (semi-)contractivity, respectively. On basis results, short-time behavior propagator norm for discrete-time is characterized by (shifted) index (scaled) index,

The construction of attractors a dissipative difference equation is usually based on compactness assumptions. In this paper, we replace them with contractivity assumptions under which the pullback and forward are identical. As consequence, degenerate to unique bounded entire solutions. an application, investigate integrodifference equations popular models in theoretical ecology.

The study of the positive invariance and contractivity properties of polyhedral sets with respect to (w.r.t) linear systems subject to control saturation is addressed. The analysis of the nonlinear behavior of the closed-loop saturated system is made by dividing the state space in regions of saturation. In each one of these regions, the system evolution can be represented by the that of a linea...

Contraction theory is a powerful tool for proving asymptotic properties of nonlinear dynamical systems including convergence to an attractor and entrainment to a periodic excitation. We consider three generalizations of contraction with respect to a norm that allow contraction to take place after small transients in time and/or amplitude. These generalized contractive systems (GCSs) are useful ...

Consider a proper metric space X and a sequence (Fn)n≥0 of i.i.d. random continuous mappings X → X. It induces the stochastic dynamical system (SDS) X n = Fn ◦ · · · ◦ F1(x) starting at x ∈ X. In this and the subsequent paper, we study existence and uniqueness of invariant measures, as well as recurrence and ergodicity of this process. In the present first part, we elaborate, improve and comple...