Open conformal systems and perturbations of transfer operators

DOI10.1007/978-3-319-72179-8zbMath1397.37001OpenAlexW2767786342MaRDI QIDQ1692404

Mariusz Urbański, Mark Pollicott

Publication date: 9 January 2018

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-72179-8

zbMATH Keywords

singular perturbationPerron-Frobenius operatorescape ratesurvivor setconformal dynamical systemopen dynamical system, Hausdorff dimension

Mathematics Subject Classification ID

Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02) Smooth dynamical systems: general theory (37Cxx) Topological dynamics (37Bxx)

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Map lattices coupled by collisions: hitting time statistics and collisions per lattice unit ⋮ The bifurcation locus for numbers of bounded type ⋮ Transfer operators and conditional expectations: the non-commutative case, the case of mu-Brownian motions and white noise space setting ⋮ Hitting and escaping statistics: mixing, targets and holes ⋮ Volume growth for infinite graphs and translation surfaces ⋮ Escape rate and conditional escape rate from a probabilistic point of view ⋮ Renewal theorems for processes with dependent interarrival times ⋮ Asymptotic escape rates and limiting distributions for multimodal maps ⋮ The bifurcation set as a topological invariant for one-dimensional dynamics

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