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 language | English |
|---|---|
| Pages (from-to) | 291-317 |
| Number of pages | 27 |
| Journal | Ergodic Theory and Dynamical Systems |
| Volume | 28 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Feb 1 2008 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics
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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 journal › Article
}
TY - JOUR
T1 - Decay of correlations in suspension semi-flows of angle-multiplying maps
AU - Tsujii, Masato
PY - 2008/2/1
Y1 - 2008/2/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=38149062939&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=38149062939&partnerID=8YFLogxK
U2 - 10.1017/S0143385707000430
DO - 10.1017/S0143385707000430
M3 - Article
AN - SCOPUS:38149062939
VL - 28
SP - 291
EP - 317
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
SN - 0143-3857
IS - 1
ER -