Opuscula Math. 36, no. 4 (2016), 499-512
http://dx.doi.org/10.7494/OpMath.2016.36.4.499

 
Opuscula Mathematica

Entropy of foliations with leafwise Finsler structure

Ilona Michalik
Szymon Walczak

Abstract. 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.

Keywords: geometric entropy, leafwise Finsler structure.

Mathematics Subject Classification: 58B20, 37A35, 53C12, 53C60.

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  • Ilona Michalik
  • AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, Poland
  • Szymon Walczak
  • Communicated by P.A. Cojuhari.
  • Received: 2015-09-12.
  • Revised: 2016-01-06.
  • Accepted: 2016-01-06.
  • Published online: 2016-04-01.
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Cite this article as:
Ilona Michalik, Szymon Walczak, Entropy of foliations with leafwise Finsler structure, Opuscula Math. 36, no. 4 (2016), 499-512, http://dx.doi.org/10.7494/OpMath.2016.36.4.499

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