Remarks on definitions of periodic points for nonautonomous dynamical system

Periodic Solutions of Second-order Nonautonomous Dynamical Systems

Remarks on Bounded Solutions for Some Nonautonomous Ode

A Borsuk–Ulam type argument is used in order to prove existence of nontrivial bounded solutions to some nonautonomous linear differential equations.

Coherent sets for nonautonomous dynamical systems

We describe a mathematical formalism and numerical algorithms for identifying and tracking slowly mixing objects in nonautonomous dynamical systems. In the autonomous setting, such objects are variously known as almost-invariant sets, metastable sets, persistent patterns, or strange eigenmodes, and have proved to be important in a variety of applications. In this current work, we explain how to...

Remarks on Finding Critical Points

In the course of writing a chapter of a book we observed some simple facts dealing with the Palais SmaIe property and critical points of functions. Some of these facts turned out to be known, though not well-known, and we think it worthwhile to make them more available. In addition, we present some other recent results which we believe will prove to be useful-in particular, a result of Ghoussou...

State Space Decomposition for Nonautonomous Dynamical Systems

Decomposition of state spaces into dynamically different components is helpful for the understanding of dynamical behaviors of complex systems. A Conley type decomposition theorem is proved for nonautonomous dynamical systems defined on a non-compact but separable state space. Namely, the state space can be decomposed into a chain recurrent part and a gradient-like part. This result applies to ...