Generalized Farey trees, transfer operators and phase transitions

Knauf A, Degli Esposti M, Isola S (2007)

Publication Type: Journal article, Original article

Publication year: 2007


Publisher: Springer Verlag (Germany)

Book Volume: 275

Pages Range: 297--329

Journal Issue: 2

DOI: 10.1007/s00220-007-0294-3


We consider a family of Markov maps on the unit interval, interpolating between the tent map and the Farey map. The latter is not uniformly expanding. Each map being composed of two fractional linear transformations, the family generalizes many particular properties which for the case of the Farey map have been successfully exploited in number theory. We analyze the dynamics through the spectral properties of the generalized transfer operator. Application of the thermodynamic formalism to the family reveals first and second order phase transitions and unusual properties like positivity of the interaction function.

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Knauf, A., Degli Esposti, M., & Isola, S. (2007). Generalized Farey trees, transfer operators and phase transitions. Communications in Mathematical Physics, 275(2), 297--329.


Knauf, Andreas, Mirko Degli Esposti, and Stefano Isola. "Generalized Farey trees, transfer operators and phase transitions." Communications in Mathematical Physics 275.2 (2007): 297--329.

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