Recurrent and periodic points for isometries of L spaces

Ege Fujikawa, Katsuhiko Matsuzaki

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We study the action of isometries on metric spaces. In particular, we consider the recurrent set of the bilateral shift operator on the Banach space L (ℤ), and prove that the set of periodic points is not dense in the recurrent set. Then we apply this result to investigating the dynamics of Teichmüller modular groups acting on infinite dimensional Teichmüller spaces as well as composition operators acting on Hardy spaces. Indiana University Mathematics Journal

Original languageEnglish
Pages (from-to)975-997
Number of pages23
JournalIndiana University Mathematics Journal
Volume55
Issue number3
DOIs
Publication statusPublished - 2006
Externally publishedYes

Fingerprint

Recurrent Point
L-space
Periodic Points
Isometry
Shift Operator
Modular Group
Infinite-dimensional Spaces
Composition Operator
Hardy Space
Metric space
Banach space

Keywords

  • Bilateral shift operator
  • Composition operator
  • Hardy space
  • Teichmüller modular group
  • Teichmüller space

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Recurrent and periodic points for isometries of L spaces. / Fujikawa, Ege; Matsuzaki, Katsuhiko.

In: Indiana University Mathematics Journal, Vol. 55, No. 3, 2006, p. 975-997.

Research output: Contribution to journalArticle

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