Shadowing for nonuniformly hyperbolic maps in Hilbert spaces (Q6557852)

There are extensive applications for shadowing lemma and closing lemma in the qualitative theory of dynamical systems.\NThe authors study a shadowing lemma for nonuniformly hyperbolic maps in Hilbert spaces. \NWith regard to \(\mathcal{C}^2\) nonuniformly hyperbolic maps \((f, \mu)\) in separable Hilbert space \(H\), having the shadowing property, the authors prove that the positive Lyapunov exponents of hyperbolic ergodic measure \(\mu\) can be approximated by positive Lyapunov\Nexponents of atomic measures on hyperbolic periodic orbits. As an application, they provide the upper estimation of metric entropy by using the exponential growth rate of the number of periodic points.