Renormalization of circle diffeomorphisms with a break-Type singularity

Habibulla Akhadkulov, Mohd. Salmi Md. Noorani, Sokhobiddin Akhatkulov

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Let f be an orientation-preserving circle diffeomorphism with an irrational rotation number and with a break point that is, its derivative has a jump discontinuity at this point. Suppose that satisfies a certain Zygmund condition dependent on a parameter We prove that the renormalizations of f are approximated by Möbius transformations in C 1-Topology if and in C 2-Topology if Moreover, it is shown that, in case of the coefficients of Möbius transformations get asymptotically linearly dependent. Further, consider two circle diffeomorphisms with a break point, with the same size of the break and satisfying Zygmund condition with We prove that, under a certain technical condition on rotation numbers, the renormalizations of these diffeomorphisms approach each other in C 2-Topology.

Original languageEnglish
Pages (from-to)2687-2717
Number of pages31
JournalNonlinearity
Volume30
Issue number7
DOIs
Publication statusPublished - 23 May 2017

Fingerprint

Diffeomorphisms
Renormalization
Circle
Rotation number
topology
Topology
Singularity
Irrational number
Dependent
Diffeomorphism
preserving
Discontinuity
discontinuity
Jump
Linearly
Derivatives
Derivative
Coefficient
coefficients

Keywords

  • 37C15
  • 37F25
  • break point
  • circle diffeomorphism
  • convergence
  • Möbius transformations
  • renormalization
  • rotation number Mathematics Subject Classification numbers: 37E10

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

Renormalization of circle diffeomorphisms with a break-Type singularity. / Akhadkulov, Habibulla; Md. Noorani, Mohd. Salmi; Akhatkulov, Sokhobiddin.

In: Nonlinearity, Vol. 30, No. 7, 23.05.2017, p. 2687-2717.

Research output: Contribution to journalArticle

Akhadkulov, Habibulla ; Md. Noorani, Mohd. Salmi ; Akhatkulov, Sokhobiddin. / Renormalization of circle diffeomorphisms with a break-Type singularity. In: Nonlinearity. 2017 ; Vol. 30, No. 7. pp. 2687-2717.
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