TEMPERATURE AND INITIAL CONDITIONS ON STRANGE REPELLERS

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Abstract
Chaotic maps generate symbol sequences whose lattice disorder may be described by a Gibbs distribution. In particular, the Gibbs distribution describes the frequency with which intervals are visited in chaotic motion on a multifractal. One of us pointed out earlier that the inverse temperature implies a choice of initial conditions of a map from a subset of the fractal that is typically unknown in advance. We show here that, for maps that generate strange repellers, almost all initial conditions belong to the infinite temperature distribution. Finite temperature Gibbs distributions therefore correspond to a set of symbol sequences that occur with measure zero.

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