Finite-time and exact Lyapunov dimension of the Henon map

Abstract

This work is devoted to further consideration of the Henon map with negative values of the shrinking parameter and the study of transient oscillations, multistability, and possible existence of hidden attractors. The computation of the finite-time Lyapunov exponents by different algorithms is discussed. A new adaptive algorithm for the finite-time Lyapunov dimension computation in studying the dynamics of dimension is used. Analytical estimates of the Lyapunov dimension using the localization of attractors are given. A proof of the conjecture on the Lyapunov dimension of self-excited attractors and derivation of the exact Lyapunov dimension formula are revisited.