We consider a dynamical systems formulation for models with an exponential scalar field and matter linear equation of state in spatially flat isotropic spacetime. In contrast to earlier work, which only considered hyperbolic fixed point analysis, we do center manifold analysis the non-hyperbolic points associated bifurcations. More importantly though, construct monotonic functions Dulac functio...

Abstract In this paper we study various aspects of porosities for conformal fractals. We first explore porosity in the general context infinite graph directed Markov systems (GDMS), and show that their limit sets are porous large (in sense category dimension) subsets. also provide natural geometric dynamic conditions under which set a GDMS is upper or mean porous. On other hand, prove if not po...

We characterize and describe the extensions of expansive Ano- sov homeomorphisms on compact spaces. As an application we obtain a stability result for Anosov systems, show construction that embeds any system inside having shadowing property pseudo orbits original space.