Eigenfunctions of the Perron–Frobenius operator and the finite-time Lyapunov exponents in uniformly hyperbolic area-preserving maps

The subleading eigenvalues and associated eigenfunctions of the Perron-Frobenius operator for 2-dimensional area-preserving maps are numerically investigated. We closely examine validity so-called Ulam method, a numerical scheme believed to provide operator, both linear nonlinear on torus. For case, second-largest investigated by calculating Fokker-Planck with sufficiently small diffusivity. On basis schemes thus established, we find that exhibit spatially inhomogeneous patterns, especially showing localization around region where unstable manifolds sparsely running. Finally, such spatial patterns eigenfunction shown be very close distribution maximal finite-time Lyapunov exponents.