Long-range order in the scaling behaviour of hyperbolic dynamical systems (Q803621)

The authors introduce a simple three-dimensional hyperbolic map to describe the effect of a linear low-pass filter on the skinny baker transformation. By solving the model analytically, they construct a suitable symbolic representation. Using the thermodynamic formalism, the authors detect various kinds of first-order phase transitions and show the long-range nature of the interactions among the spins (symbols). Such correlations arise from the tangency between eigendirections in the two- dimensional stable manifold of the map. As a result, the authors show that non-hyperbolicity is not the only source of fractal measures without exact self-similarity.