Scaling properties of \({\mathbb{Z}}^{k-1}\) actions on the circle

DOI10.1007/BF01010490zbMath0638.10035OpenAlexW2050017291MaRDI QIDQ1099212

Dieter H. Mayer

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1007/bf01010490

zbMATH Keywords

renormalization groupscalingcircle mappingalgebraic rotation numberJacobi- Perron algorithm

Mathematics Subject Classification ID

Phase transitions (general) in equilibrium statistical mechanics (82B26) Continued fractions and generalizations (11J70) Differentiable mappings in differential topology (57R35) Differentiable maps on manifolds (58C25)

Cites Work

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• Universal scaling behaviour for iterated maps in the complex plane
• Renormalization group analysis of quasi-periodicity in analytic maps
• Universal properties of the transition from quasi-periodicity to chaos in dissipative systems
• Universal properties of maps of the circle with \(\epsilon\)-singularities
• Approach to equilibrium for locally expanding maps in \({\mathbb{R}}^ k\)
• Spectral properties of certain composition operators arising in statistical mechanics
• Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)
• Quantitative universality for a class of nonlinear transformations
• The metrical theory of Jacobi-Perron algorithm
• The Jacobi-Perron algorithm its theory and application

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