Entropy of foliations with leafwise Finsler structure

• Autorzy: Michalik I. , Walczak S.

Identyfikatory

DOI

10.7494/OpMath.2016.36.4.499

• Języki publikacji: EN

Abstrakty

EN

We extend the notion of the geometric entropy of foliation to foliated manifolds equipped with leafwise Finsler structure. We study the relation between the geometric entropy and the topological entropy of the holonomy pseudogroup. The case of a foliated manifold with leafwise Randers structure is considered. In this case the estimates for one dimensional foliation defined by a vector field in terms of the topological entropy of a flow are presented.

Słowa kluczowe

EN

geometric entropy; leafwise Finsler structure

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2016
• Tom: Vol. 36, no. 4
• Strony: 499--512
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Michalik I.

• AGH University of Science and Technology Faculty of Applied Mathematics al. A. Mickiewicza 30, 30-059 Krakow, Poland

autor

Walczak S.

Bibliografia

• [1] R.L. Adler, A.G. Konheim, M.H. McAndrew, Topological entropy, Trans. Amer. Math. Soc. 114 (1965) 2, 309-319.
• [2] R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401-414.
• [3] E. Ghys, R. Langevin, P. Walczak, Entropie geometrique des feuilletages, Acta Math. 160 (1988), 105-142.
• [4] Y. Sayyari, M. Molaei, S.M. Moghayer, Entropy of continuous maps on quasi-metric spaces, preprint, arXiv:1403.2106v2.
• [5] Z. Shen, Lectures on Finsler Geometry, World Scientific, Singapore 2001.
• [6] P. Walczak, Dynamics of Foliations, Groups and Pseudogroups, Monografie Matematyczne, Vol. 64, Birkhauser, Basel 2004.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.