Phase Transitions on Strange Attractors and Fractal Aggregates

Abstract

We use a thermodynamic formalism to describe multifractal sets. A thermodynamic function, ‘free energy’ as a function of ‘temperature’, is obtained. This function may exhibit a discontinuity in some order of the derivative, indicating a phase transition. For a strange attractor of the Hénon type we find a transition from the non-singular manifold to the turnbacks. In some fractal aggregates (especially experimental) there might be a transition from the tip-structure to the fjord-structure. This can be interpreted as a screening of the fjords from the diffusing field.