A Ruelle operator for a real Julia set

DOI10.1007/BF02100007zbMath0749.58039OpenAlexW2082665526WikidataQ120825481 ScholiaQ120825481MaRDI QIDQ1182052

Peter Yuditskii, Mikhail Sodin, Genadi Levin

Publication date: 27 June 1992

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02100007

zbMATH Keywords

perturbation theoryJulia setCantor-type setFredholm determinantRuelle operatorGibbs stateLyapunov metric

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Dynamical systems with hyperbolic behavior (37D99)

Related Items (11)

Ruelle operators with rational weights for Julia sets ⋮ On explicit connections between dynamical and parameter spaces ⋮ On Mayer's conjecture and zeros of entire functions ⋮ Transversality for Critical Relations of Families of Rational Maps: An Elementary Proof ⋮ Positive transversality via transfer operators and holomorphic motions with applications to monotonicity for interval maps ⋮ Spectral structure of transfer operators for expanding circle maps ⋮ Lower bounds for the Ruelle spectrum of analytic expanding circle maps ⋮ Fixed points of the Ruelle–Thurston operator and the Cauchy transform ⋮ Transversality in the setting of hyperbolic and parabolic maps ⋮ Multipliers of periodic orbits in spaces of rational maps ⋮ On the distribution of zeros of a Ruelle zeta-function

Cites Work

• Orthogonality properties of iterated polynomial mappings
• The thermodynamic formalism for expanding maps
• Quasiconformal homeomorphisms and dynamics. I: Solution of the Fatou- Julia problem on wandering domains
• Strange objects in the complex plane
• Orthogonal polynomials on a family of Cantor sets and the problem of iterations of quadratic mappings
• Zeta-functions for expanding maps and Anosov flows
• The limit-periodic finite-difference operator on \(l^ 2(\mathbf Z)\) associated with iterations of quadratic polynomials.
• Invariant sets under iteration of rational functions
• Some connections between ergodic theory and the iteration of polynomials
• Complex analytic dynamics on the Riemann sphere
• Escape from strange repellers
• The dynamics of rational transforms: the topological picture
• Orthogonal polynomials associated with invariant measures on Julia sets
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
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