# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Sets of nondifferentiability for conjugacies between expanding interval maps

### Tom 206 / 2009

Fundamenta Mathematicae 206 (2009), 161-183 MSC: Primary 37C45; Secondary 28A80, 37A10. DOI: 10.4064/fm206-0-10

#### Streszczenie

We study differentiability of topological conjugacies between expanding piecewise $C^{1+\epsilon }$ interval maps. If these conjugacies are not $C^1$, then their derivative vanishes Lebesgue almost everywhere. We show that in this case the Hausdorff dimension of the set of points for which the derivative of the conjugacy does not exist lies strictly between zero and one. Moreover, by employing the thermodynamic formalism, we show that this Hausdorff dimension can be determined explicitly in terms of the Lyapunov spectrum. These results then give rise to a “rigidity dichotomy” for the type of conjugacies under consideration.

#### Autorzy

• Thomas JordanDepartment of Mathematics
University of Bristol
Bristol, BS8 1TW, UK
e-mail
• Marc KesseböhmerFachbereich 3–Mathematik und Informatik
Universität Bremen
D-28359 Bremen, Germany
e-mail
• Mark PollicottMathematics Institute
University of Warwick
Coventry, CV4 7AL, UK
e-mail
• Bernd O. StratmannMathematics Institute
University of St Andrews
St Andrews, KY16 9SS, Scotland
e-mail

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek