Search results for "dynamical system"
showing 10 items of 523 documents
Periodic measures and partially hyperbolic homoclinic classes
2019
In this paper, we give a precise meaning to the following fact, and we prove it: $C^1$-open and densely, all the non-hyperbolic ergodic measures generated by a robust cycle are approximated by periodic measures. We apply our technique to the global setting of partially hyperbolic diffeomorphisms with one dimensional center. When both strong stable and unstable foliations are minimal, we get that the closure of the set of ergodic measures is the union of two convex sets corresponding to the two possible $s$-indices; these two convex sets intersect along the closure of the set of non-hyperbolic ergodic measures. That is the case for robustly transitive perturbation of the time one map of a tr…
A note on the characteristic $p$ nonabelian Hodge theory in the geometric case
2012
We provide a construction of associating a de Rham subbundle to a Higgs subbundle in characteristic $p$ in the geometric case. As applications, we obtain a Higgs semistability result and a $W_2$-unliftable result.
Caractérisation des flots d' Anosov en dimension 3 par leurs feuilletages faibles
1995
AbstractWe consider Anosov flows on closed 3-manifolds. We show that if such a flow admits a weak foliation whose lifting in the universal covering is a product foliation, thenit is characterized up to topological equivalence by its weak stable foliation up to topological conjugacy. As a corollary we obtain that, up to topological equivalence and finite coverings, suspensions and geodesic flows are the unique Anosov flows on closed 3-manifolds whose weak stable foliations are transversely projective.
Sobolev homeomorphic extensions onto John domains
2020
Abstract Given the planar unit disk as the source and a Jordan domain as the target, we study the problem of extending a given boundary homeomorphism as a Sobolev homeomorphism. For general targets, this Sobolev variant of the classical Jordan-Schoenflies theorem may admit no solution - it is possible to have a boundary homeomorphism which admits a continuous W 1 , 2 -extension but not even a homeomorphic W 1 , 1 -extension. We prove that if the target is assumed to be a John disk, then any boundary homeomorphism from the unit circle admits a Sobolev homeomorphic extension for all exponents p 2 . John disks, being one sided quasidisks, are of fundamental importance in Geometric Function The…
Coordinates for quasi-Fuchsian punctured torus space
1998
We consider complex Fenchel-Nielsen coordinates on the quasi-Fuchsian space of punctured tori. These coordinates arise from a generalisation of Kra's plumbing construction and are related to earthquakes on Teichmueller space. They also allow us to interpolate between two coordinate systems on Teichmueller space, namely the classical Fuchsian space with Fenchel-Nielsen coordinates and the Maskit embedding. We also show how they relate to the pleating coordinates of Keen and Series.
Structure of the space of reducible connections for Yang-Mills theories
1990
Abstract The geometrical structure of the gauge equivalence classes of reducible connections are investigated. The general procedure to determine the set of orbit types (strata) generated by the action of the gauge group on the space of gauge potentials is given. In the so obtained classification, a stratum, containing generically certain reducible connections, corresponds to a class of isomorphic subbundles given by an orbit of the structure and gauge group. The structure of every stratum is completely clarified. A nonmain stratum can be understood in terms of the main stratum corresponding to a stratification at the level of a subbundle.
Kodaira dimension of holomorphic singular foliations
2000
We introduce numerical invariants of holomorphic singular foliations under bimeromorphic transformations of surfaces. The basic invariant is a foliated version of the Kodaira dimension of compact complex manifolds.
The Rationality Criterion
2014
In this chapter we explain a remarkable theorem of Miyaoka [32] which asserts that a foliation whose cotangent bundle is not pseudoeffective is a foliation by rational curves. The original Miyaoka’s proof can be thought as a foliated version of Mori’s technique of construction of rational curves by deformations of morphisms in positive characteristic [33].
Linearization of complex hyperbolic Dulac germs
2021
We prove that a hyperbolic Dulac germ with complex coefficients in its expansion is linearizable on a standard quadratic domain and that the linearizing coordinate is again a complex Dulac germ. The proof uses results about normal forms of hyperbolic transseries from another work of the authors.
Equidistribution and Counting of Quadratic Irrational Points in Non-Archimedean Local Fields
2019
We use these results to deduce equidistribution and counting results of quadratic irrational elements in non-Archimedean local fields.