Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps (Q926804)

The aim of the article is to develop theory and numerics in the uniformly hyperbolic setting to aid the dynamical interpretation of eigendistributions corresponding to large eigenvalues of the Perron-Frobenius operator \(\mathcal{P}:\mathcal{B}(M)\to \mathcal{B}(M),\mathcal{P}f(x)=f(T^{-1}x)| \det DT^{-1}(x)| \) of an uniformly hyperbolic dynamical system defined by a transitive \(C^2\) Anosov or Axiom A diffeomorphism \(T\) mapping smooth compact manifold \(M\) onto itself, \(\mathcal{B}(M)\) is a suitable Banach space. The main attention is payed to the manipulation of numerical eigendistribution approximations to provide an useful dynamical information.