Dimension of weakly expanding points for quadratic maps

Dimension of Weakly Expanding Points for Quadratic Maps

— For the real quadratic map Pa(x) = x2 + a and a given > 0 a point x has good expansion properties if any interval containing x also contains a neighborhood J of x with Pn a |J univalent, with bounded distortion and B(0, ) ⊆ Pn a (J) for some n ∈ N. The -weakly expanding set is the set of points which do not have good expansion properties. Let α denote the negative fixed point and M the first ...

Srb Measures for Weakly Expanding Maps

We construct SRB measures for endomorphisms satisfying conditions far weaker than the usual non-uniform expansion. As a consequence, the definition of a non-uniformly expanding map can be weakened. We also prove the existence of an absolutely continuous invariant measure for local diffeomorphisms, only assuming the existence of hyperbolic times for Lebesgue almost every point in the manifold.

A RESULT ON FIXED POINTS FOR WEAKLY QUASI-CONTRACTION MAPS IN METRIC SPACES

In this paper, we give a new fixed point theorem forWeakly quasi-contraction maps in metric spaces. Our results extend and improve some fixed point and theorems in literature.    

a result on fixed points for weakly quasi-contraction maps in metric spaces

in this paper, we give a new fixed point theorem forweakly quasi-contraction maps in metric spaces. our results extend and improve some fixed point and theorems in literature.

Fixed Points of Weakly Contractive Maps and Boundedness of Orbits