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On the spectrum of the transfer operators of a one-parameter family with intermittency transition. (English) Zbl 1336.37019

Summary: We study the transfer operators for a family \(F_r:[0,1]\to[0,1]\) depending on the parameter \(r\in[0,1]\) which interpolates between the tent map and the Farey map. In particular, considering the action of the transfer operator on a suitable Hilbert space, we can define a family of infinite matrices associated to the operators and study their spectrum by numerical methods.

MSC:

37C30 Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc.
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
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