On the Convergence to Equilibrium of Unbounded Observables Under a Family of Intermittent Interval Maps
| Autor: | Johannes Kautzsch, Marc Kesseböhmer, Tony Samuel |
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| Rok vydání: | 2015 |
| Předmět: |
Physics
Nuclear and High Energy Physics Operator (physics) 010102 general mathematics Order (ring theory) Statistical and Nonlinear Physics Dynamical Systems (math.DS) Interval (mathematics) 01 natural sciences Omega Combinatorics 010104 statistics & probability Singularity Iterated function FOS: Mathematics Farey sequence Gravitational singularity 37A40 37A25 37A50 60K05 Mathematics - Dynamical Systems 0101 mathematics Mathematical Physics |
| Zdroj: | Annales Henri Poincaré. 17:2585-2621 |
| ISSN: | 1424-0661 1424-0637 |
| DOI: | 10.1007/s00023-015-0451-8 |
| Popis: | We consider a family $${\{T_{r}: [0, 1] \circlearrowleft \}_{r\in[0, 1]}}$$ of Markov interval maps interpolating between the tent map $${T_{0}}$$ and the Farey map $${T_{1}}$$ . Letting $${\mathcal{P}_{r}}$$ denote the Perron–Frobenius operator of $${T_{r}}$$ , we show, for $${\beta \in [0, 1]}$$ and $${\alpha \in (0, 1)}$$ , that the asymptotic behaviour of the iterates of $${\mathcal{P}_{r}}$$ applied to observables with a singularity at $${\beta}$$ of order $${\alpha}$$ is dependent on the structure of the $${\omega}$$ -limit set of $${\beta}$$ with respect to $${T_{r}}$$ . The results presented here are some of the first to deal with convergence to equilibrium of observables with singularities. |
| Databáze: | OpenAIRE |
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