Invariant Sets for Windows

Abstract

This book is devoted to strange nonchaotic attractors-dynamical states that appear in quasiperiodically forced systems and lie in between chaos and order. They have been discovered in a seminal paper by Grebogi, Ott, Pelikan, and Yorke [1984]. Since then these objects have been observed experimentally and have been found in different models. Although a complete mathematical description of SNAs is still to be done, many of their properties are well understood on a physical level, and this is the subject of our book. We try to describe here strange nonchaotic attractors on a level accessible for graduate students having a basic knowledge of nonlinear dynamics. We show how different tools of nonlinear dynamics, like bifurcation analysis and Lyapunov exponents, work for these systems. Although our presentation mainly relies on our works during the last decade, we also have tried to review many papers appearing in this field.

Towards scenarios of chaos appearance in three-dimensional maps

“…2 При этом многие компьютерные иллюстрации в статье были получены с помощью программного комплекса WinSet [19,20].…”

Automatic Generation of Aesthetic Patterns with the Use of Dynamical Systems

“…Many examples of dynamical systems are known [6], but we are mainly interested in those which produce geometric patterns that can be recognized as aesthetic ones. Now, we present the examples of such dynamical systems:…”

On two-frequency quasi-periodic perturbations of systems close to two-dimensional Hamiltonian ones with a double limit cycle

“…Possible phase portraits of the averaged system (4.10) obtained using the WInSet software [34,35] are shown in Figures 1-3.…”