Abstract:

Trace formulas relate short time dynamics (unstable periodic orbits) to long time invariant state space densities (natural measure). Higer dimensional dynamics requires inclusion into trace formulas of higher-dimensional compact invariant sets, such as partially hyperbolic invariant tori. A trace formula for partially hyperbolic $(N+1)$-dimensional compact manifolds invariant under a global continuous symmetry is derived here. In this extension of "periodic orbit" theory there are no or very few periodic orbits - the relative periodic orbits that the trace formula has support on are "quasiperiodic," almost never eventually periodic.

References:
[1] P. Cvitanović, Continuous symmetry reduced trace formulas (in preparation)
[2] P. Cvitanović, ChaosBook.org, rough draft of chapter "Continuous symmetry reduction"