Symbolic dynamics generated by a hybrid chaotic systems

We consider piecewise defined differential dynamical systems which can be analysed through symbolic dynamics and transition matrices. We have a continuous regime, where the time flow is characterized by an ordinary differential equation (ODE) which has explicit solutions, and the singular regime, where the time flow is characterized by an appropriate transformation. The symbolic codification is given through the association of a symbol for each distinct regular system and singular system. The transition matrices are then determined as linear approximations to the symbolic dynamics. We analyse the dependence on initial conditions, parameter variation and the occurrence of global strange attractors.

A symbolic approach to nonlinearly perturbed heat equation

We consider a system described by the linear heat equation with adiabatic boundary conditions which is perturbed periodicaly. This perturbation is nonlinear and is characterized by a one-parameter family of quadratic maps. The system, depending on the parameters, presents very complex behaviour. We introduce a symbolic framework to analyze the system and resume its most important features.

José Rodrigues Santos de Sousa Ramos (1948-2007): The diversity of dynamical systems

José Rodrigues Santos de Sousa Ramos, mathematician of great merit, passed away on January 1st, 2007, in Lisbon. He was buried in Sobral da Adiça. His death was a huge loss for the development of mathematics in Portugal. The course of time will increase the dimension of this loss. Therefore, we dedicated this theme issue on Dynamical Systems to recall his memory and underline his work. We never forget you.