Entropy and ergodic probability for differentiable dynamical systems and their bundle extensions (Q861952)

The authors show that the entropy of a \(C^1\) vector field or a \(C^1\) diffeomorphism of an \(n\)-dimensional manifold is equal to the entropy of its bundle extensions. Moreover, they prove that each ergodic probability with simple Lyapunov spectrum has at most \(2^n n!\) covering probabilities on each bundle extension.