Statistical properties of certain 2D mostly expanding fast-slow systems

Vortrag von Dr. Nicholas Fleming

Datum: 17.12.25  Zeit: 13.30 - 14.30  Raum: Y27H28

This is joint work with Jacopo De Simoi and Kasun Fernando. We consider a class of sufficiently smooth partially hyperbolic fast-slow systems on the 2-torus, obtained by a size ε perturbation of a trivial extension of a family of expanding circle maps. Such fast-slow systems obey an averaging principle: at time-scale 1/ε the slow part is approximated by the solution of an ODE. Assuming that this ODE has exactly one sink and both Lyapunov exponents of the system are positive, we prove the system admits a unique physical (SRB) measure. Moreover, we establish exponential decay of correlations, with explicit, nearly optimal bounds on the decay rate.
This result provides a ‘mostly expanding’ counterpart to the work of De Simoi and Liverani, who treated such systems in the ‘mostly contracting’ case (i.e., where there is one negative Lyapunov exponent).