Hausdorff dimension and asymptotic cycles

We carry out a multifractal analysis for the asymptotic cycles for compact Riemann surfaces of genus g > 2. This describes the set of unit tangent vectors for which the associated orbit has a given asymptotic cycle in homology.

[1]  V. Arnold Mathematical Methods of Classical Mechanics , 1974 .

[2]  Y. Pesin,et al.  Dimension theory in dynamical systems , 1997 .

[3]  O. Jenkinson Rotation, entropy, and equilibrium states , 2001 .

[4]  R. Bowen Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms , 1975 .

[5]  Y. Pesin,et al.  Multifractal Analysis of Conformal Axiom A Flows , 2001 .

[6]  John Franks,et al.  Knots, Links, and Symbolic Dynamics , 1981 .

[7]  Oliver Jenkinson Frequency Locking on the Boundary of the Barycentre Set , 2000, Exp. Math..

[8]  Rufus Bowen,et al.  SYMBOLIC DYNAMICS FOR HYPERBOLIC FLOWS. , 1973 .

[9]  H. Weiss,et al.  The multifractal analysis of Gibbs measures: Motivation, mathematical foundation, and examples. , 1997, Chaos.

[10]  D. Burago,et al.  Riemannian tori without conjugate points are flat , 1994 .

[11]  J. Schmeling,et al.  On fast Birkhoff averaging , 2003, Mathematical Proceedings of the Cambridge Philosophical Society.

[12]  V. Bangert Minimal Measures and Minimizing Closed Normal One-currents , 1999 .

[13]  D. Sullivan Cycles for the dynamical study of foliated manifolds and complex manifolds , 1976 .

[14]  F. Pirani MATHEMATICAL METHODS OF CLASSICAL MECHANICS (Graduate Texts in Mathematics, 60) , 1982 .

[15]  D. Massart Stable Norms of Surfaces: Local Structure of the Unit Ball at Rational Directions , 1997 .

[16]  L. Barreira,et al.  Higher-dimensional multifractal analysis , 2002 .

[17]  M. Ratner Markov partitions for anosov flows onn-dimensional manifolds , 1973 .

[18]  Vladimir Igorevich Arnolʹd,et al.  Les méthodes mathématiques de la mécanique classique , 1976 .

[19]  Thierry Bousch,et al.  Le poisson n'a pas d'arêtes , 2000 .