Global Bifurcations, Chaos, and Hyperchaos: Theory and Applications

This Focus Issue is devoted to modern aspects and trends in the theory of dynamical chaos, with the special aim of understanding the nature of multidimensional chaos. Decades of efforts by the world's leading scientists uncovered many features of chaotic dynamics in low-dimensional systems. However, even a slight increase in dimension reveals new and unexpected phenomena. For example, very little is known about the dynamics in situations where trajectories have more than one positive Lyapunov exponent (hyperchaos). This issue presents recent advances in these directions, both from theoretical and applied points of view. This includes the theory and applications of mixed dynamics, pseudohyperbolicity theory, heterodimensional cycles, and the interplay between dynamics and topology. Special attention is paid to the theory of global bifurcations, which is a powerful tool for the analysis of multidimensional chaotic dynamics. This theory was, to a large extent, developed in the school of Leonid Shilnikov to whom we dedicate this Focus Issue.

Guest Editors: Dimitry Turaev, Sergey Gonchenko, Andrey Shilnikov, and Alexey Kazakov