A semi-classical analysis with wave packets for the Ruelle-Pollicott spectrum of hyperbolic dynamics

Uniformly hyperbolic dynamics (Anosov, Axiom A) have “sensitivity toinitial conditions” and manifest “determinist chaotic behavior”,e.g. mixing, statistical properties etc. The generator of theevolution operator (the “transfer operator”) has a discrete spectrum,called "Ruelle-Pollicott resonances" which describes the effectiveconvergence and fluctuations towards equilibrium. We will present amethod of analysis using decomposition into wave packets (orwavelets) that gives new results. This method is similar to the“Weyl-Hörmander phase-space metric method”. We will also discussnumerical computation of the spectrum. Joint work with Masato Tsujii.