GEOMETRICAL AND MEASURE-THEORETIC STRUCTURES OF MAPS WITH A MOSTLY EXPANDING CENTER

Geometric and Measure-theoretical Structures of Maps with Mostly Contracting Center

We show that every diffeomorphism with mostly contracting center direction exhibits a geometric-combinatorial structure, which we call skeleton, that determines the number, basins and supports of the physical measures. Furthermore, the skeleton allows us to describe how the physical measure bifurcate as the diffeomorphism changes. In particular, we use this to construct examples with any given ...

a comparison of teachers and supervisors, with respect to teacher efficacy and reflection

supervisors play an undeniable role in training teachers, before starting their professional experience by preparing them, at the initial years of their teaching by checking their work within the proper framework, and later on during their teaching by assessing their progress. but surprisingly, exploring their attributes, professional demands, and qualifications has remained a neglected theme i...

Gibbs-markov Structures and Limit Laws for Partially Hyperbolic Attractors with Mostly Expanding Central Direction

— We consider a partially hyperbolic set K on a Riemannian manifold M whose tangent space splits as TKM = E cu⊕Es, for which the centre-unstable direction E expands non-uniformly on some local unstable disk. We show that under these assumptions f induces a Gibbs-Markov structure. Moreover, the decay of the return time function can be controlled in terms of the time typical points need to achiev...

GIBBS-MARKOV STRUCTURES AND LIMIT LAWS FOR PARTIALLY HYPERBOLIC ATTRACTORS WITH MOSTLY EXPANDING CENTRAL DIRECTION by

— We consider a partially hyperbolic set K on a Riemannian manifold M whose tangent space splits as TKM = Ecu⊕Es, for which the centre-unstable direction E expands non-uniformly on some local unstable disk. We show that under these assumptions f induces a Gibbs-Markov hyperbolic structure. Moreover, the decay of the return time function can be controlled in terms of the time typical points need...

Invariant Measure for Multidimensional Expanding Maps 1 Contents