Shadowing properties of random hyperbolic sets (Q2888823)

Let \(M\) be a finite-dimensional closed manifold, let \((\Omega, P)\) be a probability space, and let \(\sigma:\Omega\to\Omega\) be a \(P\)-invariant, ergodic, invertible transformation. A random dynamical system is a mapping \(F:{\mathbb Z}\times\Omega\times M\to M\) such that, for any \(m,n\in{\mathbb Z}\) and \(\omega\in\Omega\), (i) \(F(0,\omega,\cdot)=\text{Id}\); (ii) \(F(n+m,\omega,\cdot)=F(n,\sigma^m(\omega),\cdot)F(m,\omega,\cdot)\); (iii) \(F(n,\omega,\cdot)\) is a diffeomorphism.NEWLINENEWLINEThe authors define a hyperbolic set of \(F\) and prove that \(F\) has the Lipschitz shadowing property on a hyperbolic set.