ar X iv : m at h - ph / 9 80 50 19 v 1 2 0 M ay 1 99 8 The Definition and Measurement of the Topological Entropy per Unit Volume in Parabolic PDE ’ s

ar X iv : m at h - ph / 9 80 50 04 v 1 5 M ay 1 99 8 Five - Dimensional Tangent Vectors in Space - Time

ar X iv : m at h / 99 08 08 0 v 1 [ m at h . D S ] 1 6 A ug 1 99 9 Topological Entropy and ε - Entropy for Damped Hyperbolic Equations

We study damped hyperbolic equations on the infinite line. We show that on the global attracting set G the ε-entropy (per unit length) exists in the topology of W 1,∞. We also show that the topological entropy per unit length of G exists. These results are shown using two main techniques: Bounds in bounded domains in position space and for large momenta, and a novel submultiplicativity argument...

ar X iv : 0 90 5 . 26 80 v 1 [ m at h . D S ] 1 6 M ay 2 00 9 LYAPUNOV SPECTRUM OF ASYMPTOTICALLY SUB - ADDITIVE POTENTIALS

For general asymptotically sub-additive potentials (resp. asymptotically additive potentials) on general topological dynamical systems, we establish some variational relations between the topological entropy of the level sets of Lyapunov exponents, measuretheoretic entropies and topological pressures in this general situation. Most of our results are obtained without the assumption of the exist...

ar X iv : h ep - l at / 9 80 50 06 v 1 8 M ay 1 99 8 Studies in Random Geometries : Hyper - Cubic Random Surfaces and Simplicial Quantum Gravity

We analyze two models of random geometries : planar hyper-cubic random surfaces and four dimensional simplicial quantum gravity. We show for the hyper-cubic random surface model that a geometrical constraint does not change the critical properties of the model compared to the model without this constraint. We analyze the phase diagram for the model with extrinsic curvature. For four dimensional...

ar X iv : h ep - l at / 9 80 50 18 v 2 2 0 M ay 1 99 8 The Ginsparg - Wilson relation and local chiral random matrix theory

A chiral random matrix model with locality is constructed and examined. The Nielsen-Ninomiya no-go theorem is circumvented by the use of a generally applicable modified Dirac operator which respects the Ginsparg-Wilson relation. We observe the expected universal behaviour of the eigenvalue density in the microscopic limit.