Pruning-induced phase transition observed by a scattering method |
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Authors: | Wolfgang Breymann Jürgen Vollmer |
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Institution: | (1) Institut für Physik, Universität Basel, CH-4056 Basel, Switzerland |
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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 <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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Keywords: | Thermodynamic formalism phase transition chaotic scattering piecewise linear maps bifurcation |
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