We address the problem of necessary conditions and topological obstructions for existence robustly transitive endomorphisms on surfaces. Concretely, we show that a weak form hyperbolicity (namely, partial hyperbolicity) is condition in order to have displaying critical points, only surfaces supporting this class systems are either torus or Klein bottle. Furthermore, also prove induced action by...

15 3. Stable and unstable filtrations 17 3.1. Existence and subfoliation 17 3.2. Absolute continuity 19 4. Central Foliations 21 4.1. Normal hyperbolicity 21 4.2. Integrability of the central foliation and dynamical coherence 23 4.3. Smoothness of central leaves via normal hyperbolicity 25 4.4. Robustness of the central foliation 26 5. Intermediate Foliations 27 5.1. Nonintegrability of interme...

In many cases hyperbolicity in dynamical systems can be expressed in terms of the spectrum of some canonically associated linear operator; e.g., the linearization at a fixed point. Such a characterization is known for Anosov diffeomorphisms and flows. We construct a vector bundle map, based on the tensor product, whose spectrum is decisive for detecting the normal hyperbolicity of a flow or dif...

We present a geometric singular perturbation analysis of a chemical oscillator. Although the studied three-dimensional model is rather simple its dynamics are quite complex. In the original scaling the problem has a folded critical manifold which additionally becomes tangent to the fast bers in a region relevant to the dynamics. Thus normal hyperbolicity of the critical manifold is lost in two ...

We use explicit solutions to a drifted Laplace equation in warped product model spaces as comparison constructions to show phyperbolicity of a large class of submanifolds for p ≥ 2. The condition for p-hyperbolicity is expressed in terms of upper support functions for the radial sectional curvatures of the ambient space and for the radial convexity of the submanifold. In the process of showing ...

Elementary symmetric polynomials can be thought of as derivative polynomials of En(x) = ∏ i=1,...,n xi. Their associated hyperbolicity cones give a natural sequence of relaxations for R+. We establish a recursive structure for these cones, namely, that the coordinate projections of these cones are themselves hyperbolicity cones associated with elementary symmetric polynomials. As a consequence ...

We consider continuous SL(2, R)-cocycles over a strictly ergodic homeomorphism which fibers over an almost periodic dynamical system (generalized skew-shifts). We prove that any cocycle which is not uniformly hyperbolic can be approximated by one which is conjugate to an SO(2, R)-cocycle. Using this, we show that if a cocycle’s homotopy class does not display a certain obstruction to uniform hy...