Formulas for Lyapunov exponents
A. T. Baraviera, P. Duarte
TL;DR
This paper introduces a new series summation formula to compute Lyapunov exponents for random matrix cocycles, enhancing the ability to evaluate these exponents in complex systems.
Contribution
It derives a novel series summation formula for the average logarithm norm of matrix actions, extending Furstenberg's explicit integral formula for certain cases.
Findings
Derived a series summation formula for Lyapunov exponents.
Applied the formula to evaluate exponents of random SL(2,R)-matrix cocycles.
Provided a new computational tool for analyzing stability in dynamical systems.
Abstract
We derive a series summation formula for the average logarithm norm of the action of a matrix on the projective space. This formula is shown to be useful to evaluate some Lyapunov exponents of random -matrix cocycles, which include a special class for which H. Furstenberg had provided an explicit integral formula.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Spectral Theory in Mathematical Physics