RESONANCES OF DYNAMICAL-SYSTEMS AND FREDHOLM-RIESZ OPERATORS ON RIGGED HILBERT-SPACES

Resonances of dynamical systems are defined as the singularities of th e analytically continued resolvent of the restriction of the Frobenius -Perron operator to suitable test-function spaces. A sufficient condit ion for resonances to arise from a meromorphic continuation to the ent ire plane is that the Frobenius-Perron operator is a Fredholm-Riesz op erator on a rigged Hilbert space. After a discussion of spectral theor y in locally convex topological vector spaces, we illustrate the appro ach for a simple chaotic system, namely the Renyi map.