 9210 Aurich R., Bolte J., Matthies C., Sieber M., Steiner F.
 Crossing the Entropy Barrier of Dynamical Zeta Functions
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Feb 13, 92

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Abstract. Dynamical zeta functions
are an important tool to quantize chaotic
dynamical systems. The basic quantization rules require the
computation of the zeta functions on the real energy axis, where their
Euler product representations running over the classical periodic
orbits usually do not converge due to the
existence of the socalled entropy barrier determined by the
topological entropy of the classical system. We show that the
convergence properties of the dynamical zeta functions rewritten as
Dirichlet series are governed not only by the wellknown topological
and metric entropy, but depend crucially on subtle statistical
properties of the Maslov indices and of the multiplicities of
the periodic orbits that are measured by a new parameter for which
we introduce the notion of a {\it third entropy}. If and only if
the third entropy is nonvanishing, one can cross the entropy
barrier; if it exceeds a certain value, one can even
compute the zeta function in the physical region by means of a
convergent Dirichlet series. A simple statistical model is
presented which allows to compute the third entropy.
Four examples of
chaotic systems are studied in detail to test the model numerically.
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