Unstable entropy and unstable pressure for partially hyperbolic endomorphisms

Physical Measures for Partially Hyperbolic Surface Endomorphisms

We consider dynamical systems generated by partially hyperbolic surface endomorphisms of class Cr with one-dimensional strongly unstable subbundle. As the main result, we prove that such a dynamical system generically admits finitely many ergodic physical measures whose union of basins of attraction has total Lebesgue measure, provided that r ≥ 19.

Minimality of Strong Stable and Unstable Foliations for Partially Hyperbolic Diffeomorphisms

Entropy-expansiveness for Partially Hyperbolic Diffeomorphisms

We show that diffeomorphisms with a dominated splitting of the form Es⊕Ec⊕Eu, where Ec is a nonhyperbolic central bundle that splits in a dominated way into 1-dimensional subbundles, are entropy-expansive. In particular, they have a principal symbolic extension and equilibrium states.

Valid Inference in Partially Unstable GMM Models∗

The paper considers estimation and inference of time series GMM models where a subset of parameters are time varying. The magnitude of the time variation in the unstable parameters is such that efficient tests detect the instability with (possibly high) probability smaller than one, even in the limit. We show that for many forms of parameter instability and for a large class of GMM models, stan...

Parametrizing Unstable and Very Unstable Manifolds

Existence and uniqueness theorems for unstable manifolds are well-known. Here we prove certain refinements. Let f : (C, 0) → C be a germ of an analytic diffeomorphism, whose derivative Df(0) has eigenvalues λ1, . . . , λn such that |λ1| ≥ · · · ≥ |λk| > |λk+1| ≥ · · · ≥ |λn|, with |λk| > 1. Then there is a unique k-dimensional invariant submanifold whose tangent space is spanned by the generali...