We investigate a new type of approximation to quantum determinants, the "quantum Fredholm determinant," and test numerically the conjecture that for Axiom A hyperbolic flows such determinants have a larger domain of ...

The global constraints on chaotic dynamics induced by the analyticity of smooth flows are used to dispense with individual periodic orbits and derive infinite families of exact sum rules for several simple dynamical systems. ...

Periodic orbit theory is all effective tool for the analysis of classical and quantum chaotic systems. In this paper we extend this approach to stochastic systems, in particular to mappings with additive noise. The theory ...

The trace formula for the evolution operator associated with nonlinear stochastic flows with weak additive noise is cast in the path integral formalism. We integrate over the neighbourhood of a given saddlepoint exactly ...

Proofs that Fredholm determinants of transfer operators for hyperbolic flows are entire can be extended to a large new class of multiplicative evolution operators. We construct such operators both for the Gutzwiller ...