Anosov magnetic flows, critical values and topological entropy. Nonlinearity 15 (2008)
Abstract. We study the magnetic flow determined by a smooth Riemannian metric g and a closed 2-form Ω on a closed manifold M. If the lift of Ω to the universal cover � M is exact, we can define...
Anosov Magnetic Flows, Critical Values And Topological Entropy (2007)
Keith Burns, Gabriel P. Paternain
. We study the magnetic ow determined by a smooth Riemannian metric g and a closed 2-form on a closed manifold M . If the lift of to the universal cover f M is exact, we can dene a critical value...
Abstract. We study the magnetic ow determined by a smooth Riemannian metric g and a closed
Anosov Magnetic Flows, Critical Values And Topological Entropy (2007)
Keith Burns, Gabriel P. Paternain
We study the magnetic ow determined by a smooth Riemannian metric g and a closed 2-form on a closed manifold M . If the lift of to the universal cover M is exact, we can de ne a critical value c(g;...
Growth of the number of geodesics between points and insecurity for riemannian manifolds (2007)
A Riemannian manifold is said to be uniformly secure if there is a finite number $s$ such that all geodesics connecting an arbitrary pair of points in the manifold can be blocked by $s$ point...
On the ergodicity of partially hyperbolic systems (2005)
Pugh and Shub have conjectured that essential accessibility implies ergodicity, for a $C^2$, partially hyperbolic, volume-preserving diffeomorphism. We prove this conjecture under a mild center...
Abstract. For any ε> 0, we construct an explicit smooth Riemannian metric on the sphere S n, n ≥ 3, that is within ε of the round metric and has a geodesic for which the corresponding orbit of...
Recent results about stable ergodicity (1999)
Keith Burns, Charles Pugh, Michael Shub, Amie Wilkinson
The ergodic theory of uniformly hyperbolic, or Axiom A, dieomorphisms has been studied extensively, beginning with the pioneering work of Anosov, Sinai,
Stable Ergodicity of Skew Products (1999)
Stable ergodicity is dense among compact Lie group extensions of Anosov diffeomorphisms of compact manifolds. Under the additional assumption that the base map acts on an infranilmanifold, an...
Spheres With Positive Curvature And Nearly Dense Orbits For The Geodesic Flow. (1998)
. For any " ? 0, we construct an explicit smooth Riemannian metric on the sphere S n ; n 3, that is within " of the round metric and has a geodesic for which the corresponding orbit of the...
Stable Ergodicity and Anosov Flows (1998)
Keith Burns, Charles Pugh, Amie Wilkinson
In this note we prove that if M is a 3-manifold and ' t : M ! M is a C 2 , volume-preserving Anosov flow, then the time-1 map ' 1 is stably ergodic if and only if ' t is not a...
A Geometric Criterion For Positive Topological Entropy (1997)
. We prove that a diffeomorphism possessing a homoclinic point with a topological crossing (possibly with infinite order contact) has positive topological entropy, along with an analogous statement...
Counting geodesics on a Riemannian manifold and topological entropy of geodesic flows (1996)
Burns, Keith, Paternain, Gabriel
Let $M$ be a compact $C^{\infty}$ Riemannian manifold. Given $p$ and $q$ in $M$ and $T>0$, define $n_{T}(p,q)$ as the number of geodesic segments joining $p$ and $q$ with length $\leq T$. Ma\~n\'e...
in collaboration with
On topological Tits buildings and their classification (1987)
We define topological Tits buildings. If a topological building A satisfies some technical conditions and is irreducible, compact, locally connected and satisfies the topological equivalent of the...
Vita.
Includes vita.