Rigged Hilbert Space Approach to Spectral Analysis of the Frobenius-Perron Operator for the Tent-map

Abstract

On the basis of an unified theoretical formulation of resonances and resonance states in the rigged Hilbert spaces the spectral analysis of the Frobenius-Perron operators corresponding to the exactly solvable chaotic map has been developed. Tent map as the simplest representative of exactly solvable chaos have been studied in details in frames of the developed approach. An extension the Frobenius-Perron operator resolvent to a suitable rigged Hilbert space has been constructed in particular and the properties of the generalized spectral decomposition have been studied. Resonances and resonance projections for this map have been calculated explicitly.