In this paper we introduce the method for investigation of coupled chaotic systems using topological methods. We show that if the coupling is small then there exists independent symbolic dynamics for every coupled subsystem and in consequence the systems are not synchronized. As an example we consider coupled H enon maps. Using computer interval arithmetic we nd parameter mismatch and perturbat...

A strange attractor (SA) with symmetry group G can be mapped down to an image strange attractor SA without symmetry by a smooth mapping with singularities. The image SA can be lifted to many distinct structurally stable strange attractors, each equivariant under G, all with the same image SA. If the symbolic dynamics of the image SA requires s symbols sigma(1),sigma(2), em leader,sigma(s), then...

We give an overview of the field of symbolic dynamics: its history, applications and basic definitions and examples.

Recent progress of symbolic dynamics of oneand especially two-dimensional maps has enabled us to construct symbolic dynamics for systems of ordinary differential equations (ODEs). Numerical study under the guidance of symbolic dynamics is capable to yield global results on chaotic and periodic regimes in systems of dissipative ODEs which cannot be obtained neither by purely analytical means nor...