21 Nov 2001

In the second lecture we consider a continuous action of commutative group G on a topological space X. Collection of topological entropies h(g) for every g from G can be seen as a pseudonorm on G. This situation arises for instance in the case of Liouville integrable Hamiltonian systems on a symplectic manifold M²ⁿ. Then G=Rⁿ and the corresponding Poisson action is defined by shifts along Hamiltonian flows. We exhibit an example of integrable system such that the corresponding pseudonorm on Rⁿ is non-degenerate (norm). We also explain how the particular entropies h(g) are connected to the entropy of the group G and other adjacent results.