On the relaxation time of Gauss' continued-fraction map. I: The Hilbert space approach (Koopmanism)

DOI10.1007/BF01009039zbMath0658.10057OpenAlexW2000105669MaRDI QIDQ1111602

S. H. Smith

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1007/bf01009039

zbMATH Keywords

relaxation timetrace formulasisometric operatorcontinued-fraction

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Equilibrium statistical mechanics (82B99) Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. (11K16) Ergodic theory (37A99)

Related Items (16)

Invariant densities for random continued fractions ⋮ Statistical properties of chaos demonstrated in a class of one-dimensional maps ⋮ On the location of poles of Ruelle's zeta-function ⋮ POSITIVE DILATIONS OF PIECEWISE MONOTONIC MARKOV MAPS ⋮ On the relaxation time of Gauss' continued-fraction map. II: The Banach space approach (Transfer operator method) ⋮ Haas-Molnar continued fractions and metric Diophantine approximation ⋮ Continued fraction algorithms, functional operators, and structure constants ⋮ The random continued fraction transformation ⋮ Estimates of the rate of convergence in the von Neumann and Birkhoff ergodic theorems ⋮ Ergodic properties of a kicked damped particle ⋮ Mayer's transfer operator and representations of \(\mathrm{GL}_{2}\) ⋮ Continued fraction Cantor sets, Hausdorff dimension, and functional analysis ⋮ Spectral analysis for the Gauss problem on continued fractions ⋮ On the thermodynamic formalism for the Gauss map ⋮ Dynamics of continued fractions with periodic constraints ⋮ Supersymmetric Bianchi type IX cosmology

Cites Work

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• On the approximation of invariant measures for continued fractions
• The metrical theory of Jacobi-Perron algorithm
• Über Einen Kusminschen Satz
• On the theorem of Gauss-Kusmin-Lévy and a Frobenius-type theorem for function spaces

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