Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

PERIODIC POINTS AND SHADOWING PROPERTY FOR GENERIC LEBESGUE MEASURE PRESERVING INTERVAL MAPS

Abstract : We show that for the generic continuous maps of the interval and circle which preserve the Lebesgue measure it holds for each k ≥ 1 that the set of periodic points of period k is a Cantor set of Hausdorff dimension zero and of upper box dimension one. Furthermore, building on this result, we show that there is a dense collection of transitive Lebesgue measure preserving interval map whose periodic points have full Lebesgue measure and whose periodic points of period k have positive measure for each k ≥ 1. Finally, we show that the generic continuous maps of the interval which preserve the Lebesgue measure satisfy the shadowing and periodic shadowing property.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-03181370
Contributor : Serge Troubetzkoy <>
Submitted on : Friday, April 9, 2021 - 9:10:59 AM
Last modification on : Saturday, April 10, 2021 - 3:27:44 AM

Files

Interval.v2.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03181370, version 2
  • ARXIV : 2103.14309

Citation

Jernej Činč, Jozef Bobok, Piotr Oprocha, Serge Troubetzkoy. PERIODIC POINTS AND SHADOWING PROPERTY FOR GENERIC LEBESGUE MEASURE PRESERVING INTERVAL MAPS. 2021. ⟨hal-03181370v2⟩

Share

Metrics

Record views

54

Files downloads

10