convex hyperbolic spaces Muhammad Aqeel Ahmad Khan, Ulrich Kohlenbach2,∗ Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan Department of Mathematics, Technische Universitat Darmstadt, Schlossgartenstrasse 7, 64289 Darmstadt, Germany December 7, 2012 Abstract: The purpose of this paper is to extract an explicit effective and uniform bound on the rate of...

We consider finite families of SL(2,R) matrices whose products display uniform exponential growth. These form open subsets of (SL(2,R)), and we study their components, boundary, and complement. We also consider the more general situation where the allowed products of matrices satisfy a Markovian rule.

This paper provides a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the Krasnosel’skiı̆–Mann iterations of such mappings. The latter were found using methods from logic and the paper continues a case study in the general program of extracting effective data from prima-facie ineffective proofs in the fixed po...

We develop high-resolution shock-capturing numerical schemes for hyperbolic systems with relaxation. In such systems the relaxation time may vary from order-1 to much less than unity. When the relaxation time is small, the relaxation term becomes very strong and highly stiff, and underresolved numerical schemes may produce spurious results. Usually one cannot decouple the problem into separate ...

We show differentiability of a class of Geroch’s volume functions on globally hyperbolic manifolds. Furthermore, we prove that every volume function satisfies a local anti-Lipschitz condition over causal curves, and that locally Lipschitz time functions which are locally antiLipschitz can be uniformly approximated by smooth time functions with timelike gradient. Finally, we prove that in stably...

We consider C Hénon-like families of diffeomorphisms of R and study the boundary of the region of parameter values for which the nonwandering set is uniformly hyperbolic. Assuming sufficient dissipativity, we show that the loss of hyperbolicity is caused by a first homoclinic or heteroclinic tangency and that uniform hyperbolicity estimates hold uniformly in the parameter up to this bifurcation...

Global weak solutions of a strictly hyperbolic system of balance laws in one-space dimension were constructed (cf. Christoforou [C]) via the vanishing viscosity method under the assumption that the source term g is dissipative. In this article, we establish sharp estimates on the uniformly Lipschitz semigroup P generated by the vanishing viscosity limit in the general case which includes also n...

We investigate the average-case complexity of decision problems for finitely generated groups, in particular the word and membership problems. Using our recent results on " generic-case complexity " we show that if a finitely generated group G has the word problem solv-able in subexponential time and has a subgroup of finite index which possesses a non-elementary word-hyperbolic quotient group,...

A sequence of diffeomorphisms along compact Riemannian manifolds is Anosov family if the tangent bundle split into expanding and contracting subspaces. For a certain class families, we construct Markov partitions provide an associated symbolic representation which given by non-stationary subshift finite type (NSFT). Moreover, induced coding on each component NSFT shares several properties with ...