Bifurcating Continua in Infinite Dimensional Dynamical Systems and Applications to Differential Equations

Observing Infinite-dimensional Dynamical Systems

We study the extent to which properties of infinite-dimensional dynamical systems can be accurately detected by examining observations of such systems. Let H be a separable Hilbert space. Let f : H → H be a map and let A ⊂ H be a compact set satisfying f(A) = A. We prove that for almost every (in the sense of prevalence) continuous observable φ : H → RM , if f induces a map f̄ satisfying f̄ ◦ φ =...

Dynamical Systems and Differential Equations

In this manuscript we introduce some important concepts concerning dynamical systems theory. We devote special attention to studying differential equations from a dynamical systems viewpoint. The introduced concepts are illustrated by examples.

On Two-parameter Dynamical Systems and Applications

In this note some useful properties of strongly continuous two-parameter semigroups of operators are studied, an exponential formula for two-parameter semigroups of operators on Banach spaces is obtained and some applied examples of two-parameter dynamical systems are discussed

The Dynamical Systems Approach to Differential Equations

This harmony that human intelligence believes it discovers in nature —does it exist apart from that intelligence? No, without doubt, a reality completely independent of the spirit which conceives it, sees it or feels it, is an impossibility. A world so exterior as that, even if it existed, would be forever inaccessible to us. But what we call objective reality is, in the last analysis, that whi...

Applications of Probability to Partial Differential Equations and Infinite Dimensional Analysis