Linearization of Quasiperiodically Forced Circle Flows Beyond Brjuno Condition

Raphaël Krikorian; Jing Wang; Jiangong You; Qi Zhou

doi:10.1007/s00220-017-3021-8

Linearization of Quasiperiodically Forced Circle Flows Beyond Brjuno Condition

Raphaël Krikorian
, Jing Wang
, Jiangong You
, Qi Zhou

CY Cergy Paris Université
Department of Mathematics
Nanjing University of Science and Technology
Chern Institute of Mathematics
Department of Mathematics
Nanjing University

Research output: Contribution to journal › Article › peer-review

23 Citations (Scopus)

Abstract

We prove that an analytic quasiperiodically forced circle flow with a not super-Liouvillean base frequency and which is close enough to some constant rotation is C^∞ rotations reducible, provided its fibered rotation number is Diophantine with respect to the base frequency. As a corollary, we obtain that among such systems, the linearizable ones and those displaying mode-locking are locally dense for the C^∞-topology.

Original language	English
Pages (from-to)	81-100
Number of pages	20
Journal	Communications in Mathematical Physics
Volume	358
Issue number	1
DOIs	https://doi.org/10.1007/s00220-017-3021-8
Publication status	Published - 1 Feb 2018
Externally published	Yes

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abstract = "We prove that an analytic quasiperiodically forced circle flow with a not super-Liouvillean base frequency and which is close enough to some constant rotation is C∞ rotations reducible, provided its fibered rotation number is Diophantine with respect to the base frequency. As a corollary, we obtain that among such systems, the linearizable ones and those displaying mode-locking are locally dense for the C∞-topology.",

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AB - We prove that an analytic quasiperiodically forced circle flow with a not super-Liouvillean base frequency and which is close enough to some constant rotation is C∞ rotations reducible, provided its fibered rotation number is Diophantine with respect to the base frequency. As a corollary, we obtain that among such systems, the linearizable ones and those displaying mode-locking are locally dense for the C∞-topology.

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Linearization of Quasiperiodically Forced Circle Flows Beyond Brjuno Condition

Abstract

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