Bifurcations, robustness and shape of attractors of discrete dynamical systems

Minimal attractors and bifurcations of random dynamical systems

We consider attractors for certain types of random dynamical systems. These are skew-product systems whose base transformations preserve an ergodic invariant measure. We discuss definitions of invariant sets, attractors and invariant measures for deterministic and random dynamical systems. Under assumptions that include, for example, iterated function systems, but that exclude stochastic differ...

Hidden Bifurcations and Attractors in Nonsmooth Dynamical Systems

New Strange Attractors for Discrete Dynamical Systems

A discrete dynamical system in Euclideanm-space generated by the iterates of an asymptotically zero map f , satisfying |f(x)| → 0 as |x| → ∞, must have a compact global attracting set A. The question of what additional hypotheses are sufficient to guarantee that A has a minimal (invariant) subset A that is a chaotic strange attractor is answered in detail for a few types of asymptotically zero ...

The shape of attractors for 3-D dissipative dynamical systems

We introduce a new method to bound attractors of dissipative dynamical systems in phase and parameters spaces. The method is based on the determination of families of transversal surfaces (surfaces crossed by the ow in only one direction). This technique yields very restrictive geometric bounds in phase space for the attractors. It also gives ranges of parameters of the system for which no chao...

Shape of attractors for three-dimensional dissipative dynamical systems

We introduce a method to bound attractors of dissipative dynamical systems in phase and parameter spaces. The method is based on the determination of families of transversal surfaces (surfaces crossed by the flow in only one direction). This technique yields very restrictive geometric bounds in phase space for the attractors. It also gives ranges of parameters of the system for which no chaotic...