For bi-Lipschitz homeomorphisms of a compact manifold it is known that topological entropy always finite. manifolds dimension two or greater, we show that in the closure space homeomor- phisms, with respect to either H older or Sobolev topologies, entropy generically infinite. We also prove versions C1-Closing Lemma in these spaces. Finally, give examples infinite which are and/or every e...

M. Gromov introduced the mean dimension for a continuous map in late 1990’s, which is an invariant under topological conjugacy. On other hand, notion of metric dynamical system was by Lindenstrauss and Weiss 2000 this refines entropy systems with infinite entropy. In paper we will show if N n dimensional compact riemannian manifold then, any $$a\in [0,n]$$ , set consisting maps equal to dense $...

Recently Lutz [14,15] introduced a polynomial time bounded version of Lebesgue measure. He and others (see e.g. [11,13,14,15,16,17,18,20]) used this concept to investigate the quantitative structure of Exponential Time (E=DTIME (2lin)). Previously, Ambos-Spies, Fleischhack and Huwig [2,3] introduced polynomial time bounded genericity concepts and used them for the investigation of structural pr...