Robustness of symbolic dynamics and synchronization properties

In this paper we introduce the method for investigation of coupled chaotic systems using topological methods. We show that if the coupling is small th en there exists independent symbolic dynamics for every coupled subsystem a nd in consequence the systems are not synchronized. As an example we consid er coupled Henon maps. Using computer interval arithmetic we find parameter mismatch and perturbation range for which the symbolic dynamics in the Hen on system is sustained. For coupled Henon maps we compute the value of coup ling strength for which the symbolic dynamics in every subsystem survives.