Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of the Oseledet's splitting

Abstract

We consider locally minimizing measures for the conservative twist maps of the $d$-dimensional annulus or for the Tonelli Hamiltonian flows defined on a cotangent bundle $T^{\ast }M$. For weakly hyperbolic such measures (i.e. measures with no zero Lyapunov exponents), we prove that the mean distance/angle between the stable and the unstable Oseledet's bundles gives an upper bound of the sum of the positive Lyapunov exponents and a lower bound of the smallest positive Lyapunov exponent. Some more precise results are proved too.

References in corpus (2)

• The link between the shape of the Aubry-Mather sets and their Lyapunov exponents
• Green bundles, Lyapunov exponents and regularity along the supports of the minimizing measures

Cited by in corpus (1)

• Hyperbolicity of minimizers and regularity of viscosity solutions for random Hamilton-Jacobi equations