Biorthogonalization, geometric invariant properties and rate-based estimate of Lyapunov spectra

This article develops a geometric method, referred to as natural tangent dynamics with periodic biorthogonalizations (NTDPB) for obtaining both the invariant geometric (Lyapunov-Oseledec filtrations) and the statistical properties (Lyapunov spectra) of chaotic dynamical systems, in a way suitable to be generalized for low-dimensional reduction of higher-dimensional dynamical systems.