1,854 research outputs found
Dynamics and zeta functions on conformally compact manifolds
In this note, we study the dynamics and associated zeta functions of
conformally compact manifolds with variable negative sectional curvatures. We
begin with a discussion of a larger class of manifolds known as convex
co-compact manifolds with variable negative curvature. Applying results from
dynamics on these spaces, we obtain optimal meromorphic extensions of weighted
dynamical zeta functions and asymptotic counting estimates for the number of
weighted closed geodesics. A meromorphic extension of the standard dynamical
zeta function and the prime orbit theorem follow as corollaries. Finally, we
investigate interactions between the dynamics and spectral theory of these
spaces
Weak Chaos from Tsallis Entropy
We present a geometric, model-independent, argument that aims to explain why
the Tsallis entropy describes systems exhibiting "weak chaos", namely systems
whose underlying dynamics has vanishing largest Lyapunov exponent. Our argument
relies on properties of a deformation map of the reals induced by the Tsallis
entropy, and its conclusion agrees with all currently known results.Comment: 19 pages, Standard LaTeX2e, v2: addition of the last paragraph in
Section 4. Three additional refs. To be published in QScience Connec
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