Dimension Function and Phase Transition-Like Behavior in Strange Attractors

Recently introduced conservation laws for volume expansion rates are used as a tool to investigate changes in the geometric and dynamical structure of strange attractors occurring, e.g., upon variation of a parameter. The appearance of edges in the Renyi dimension function D q and metric entropy K q is an indication of such transitions. A way to classify them by introducing two new indices j q and j q + is discussed. Moreover, these critical points can be analyzed in terms of phase transitions, in the framework of the thermodynamic formalism for dynamical systems.