Covariant Lyapunov Exponents for the Mixmaster
Giovanni Imponente, Giovanni Montani
TL;DR
This paper analyzes the chaotic dynamics of the Mixmaster Universe using a covariant Hamiltonian approach, explicitly calculating Lyapunov exponents by modeling it as a billiard on the Lobachevsky plane.
Contribution
It introduces a covariant method to compute Lyapunov exponents for the Mixmaster Universe, linking its dynamics to a billiard on the Lobachevsky plane.
Findings
Lyapunov exponents are explicitly calculated.
The Mixmaster dynamics is isomorphic to a billiard on the Lobachevsky plane.
The covariant approach provides new insights into the system's chaos.
Abstract
The dynamics of the Mixmaster Universe is analized in a covariant picture via Misner--Chitre-like variables for an ADM Hamiltonian approach. The system outcomes as isomorphic to a billiard on the Lobachevsky plane and Lyapunov exponents are calculated explicitly.
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