Decay of correlations in suspension semi-flows of angle-multiplying maps

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

We consider suspension semi-flows of angle-multiplying maps on the circle for Cr ceiling functions with r3. Under a Crgeneric condition on the ceiling function, we show that there exists a Hilbert space (anisotropic Sobolev space) contained in the L2 space such that the PerronFrobenius operator for the time-t-map acts naturally on it and that the essential spectral radius of that action is bounded by the square root of the inverse of the minimum expansion rate. This leads to a precise description of decay of correlations. Furthermore, the PerronFrobenius operator for the time-t-map is quasi-compact for a Cr open and dense set of ceiling functions.

Original languageEnglish
Pages (from-to)291-317
Number of pages27
JournalErgodic Theory and Dynamical Systems
Volume28
Issue number1
DOIs
Publication statusPublished - Feb 1 2008

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Ceil or ceiling function
Decay of Correlations
Semiflow
Ceilings
Angle
CR Functions
Anisotropic Sobolev Spaces
Sobolev spaces
Hilbert spaces
Spectral Radius
Operator
Square root
Circle
Hilbert space

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Decay of correlations in suspension semi-flows of angle-multiplying maps. / Tsujii, Masato.

In: Ergodic Theory and Dynamical Systems, Vol. 28, No. 1, 01.02.2008, p. 291-317.

Research output: Contribution to journalArticle

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