  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.
