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Vertices of Mather's beta function

Published online by Cambridge University Press:  13 May 2005

OSVALDO OSUNA
OSVALDO OSUNA
Affiliation:
IFM, University of Michoacana, Edif. C-3, C.U., C.P. 58040, Morelia, Michoacán, México (e-mail: [email protected])
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Abstract

Given a Lagrangian L, Mather introduced the $\beta$-function of L, which is a convex function. Many interesting properties of the Euler–Lagrange flow can be derived from the study of the behaviour of the $\beta$-function. In this work we obtain some links between the vertices of the $\beta$-function and the Hausdorff dimension of the associated invariant measures, from which we recover a result of differentiability of the $\beta$-function.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 3 , June 2005 , pp. 949 - 955
Copyright
2005 Cambridge University Press

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