Late-time clusters of classical dipole-conserving fractons map to integrable polygonal billiards for compact interactions, to chaotic motion for non-compact interactions, and generic trajectories exhibit a Janus point with a bidirectional arrow of time.
Lyapunov exponents in constrained and unconstrained ordinary differential equations
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We discuss several numerical methods for calculating Lyapunov exponents (a quantitative measure of chaos) in systems of ordinary differential equations. We pay particular attention to constrained systems, and we introduce a variety of techniques to address the complications introduced by constraints. For all cases considered, we develop both deviation vector methods, which follow the time-evolution of the difference between two nearby trajectories, and Jacobian methods, which use the Jacobian matrix to determine the true local behavior of the system. We also assess the merits of the various methods, and discuss assorted subtleties and potential sources of error.
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Classical Fractons: Local chaos, global broken ergodicity and an arrow of time
Late-time clusters of classical dipole-conserving fractons map to integrable polygonal billiards for compact interactions, to chaotic motion for non-compact interactions, and generic trajectories exhibit a Janus point with a bidirectional arrow of time.