Theory of First Order Phase Transitions for Chaotic Attractors of Nonlinear Dynamical Systems

A theory is presented for first order phase transitions of multifractal chaotic attractors of nonhyperbolic two-dimensional maps. (These phase transitions manifest themselves as a discontinuity in the derivative with respect to q (analogous to temperature) of the fractal dimension q-spectrum, D_q (analogous to free energy).) A complete picture of the behavior associated with the phase transition is obtained.