Abstract
In hyperbolic systems, transient chaos is associated with an underlying chaotic saddle in phase space. The structure of the chaotic saddle of a class of piecewise linear, area-preserving, two-dimensional maps with overall constant Lyapunov exponents has been observed by a scattering method. The free energy obtained in this way displays a “phase transition” at β<0 in spite of the fact that no phase transition occurs in the free energy dedcued from the spectrum of Lyapunov exponents. This is possible because pruning introduces a second effective scaling exponent by creating, at each level of the approximation, particular small pieces in the incomplete Cantor set approximating the saddle. The second scaling arises for a subset of values of the control parameter that is dense in the parameter interval.
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Breymann, W., Vollmer, J. Pruning-induced phase transition observed by a scattering method. J Stat Phys 76, 1439–1465 (1994). https://doi.org/10.1007/BF02187070
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DOI: https://doi.org/10.1007/BF02187070