The limit-periodic finite-difference operator on \(l^ 2(\mathbf Z)\) associated with iterations of quadratic polynomials.

DOI10.1007/BF01026000zbMath1086.37519MaRDI QIDQ1963705

Mikhail Sodin, Peter Yuditskii

Publication date: 2 February 2000

Published in: Journal of Statistical Physics (Search for Journal in Brave)

zbMATH Keywords

Jacobi matricesconformal mapescape rateiterations of polynomialsSinai-Bowen-Ruelle measurecomblike domainsLimit periodicity

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Iteration theory, iterative and composite equations (39B12) Difference operators (39A70) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Iteration of real functions in one variable (26A18) Linear difference operators (47B39)

Related Items (5)

On the complement of the Mandelbrot set ⋮ Disconnected Julia set and rotation sets ⋮ A Ruelle operator for a real Julia set ⋮ Multipliers of periodic orbits in spaces of rational maps ⋮ On the distribution of zeros of a Ruelle zeta-function

Cites Work

• Strange objects in the complex plane
• Mellin transforms associated with Julia sets and physical applications
• The rotation number for almost periodic potentials
• Cantor spectrum and singular continuity for a hierarchical Hamiltonian
• Invariant sets under iteration of rational functions
• Complex analytic dynamics on the Riemann sphere
• The dynamics of rational transforms: the topological picture
• A CHARACTERIZATION OF THE SPECTRUM OF HILL'S OPERATOR
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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