Zobrazeno 1 - 10
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pro vyhledávání: '"Potrie, Rafael"'
Autor:
Potrie, Rafael, Ruggiero, Rafael O.
Let $(M,g)$ be a $C^{\infty}$ compact, boudaryless connected manifold without conjugate points with quasi-convex universal covering and divergent geodesic rays. We show that the geodesic flow of $(M,g)$ is $C^{2}$-structurally stable from Ma\~{n}\'{e
Externí odkaz:
http://arxiv.org/abs/2311.12979
Autor:
Fenley, Sergio R., Potrie, Rafael
Let $\mathcal{F}_1$ and $\mathcal{F}_2$ be transverse two dimensional foliations with Gromov hyperbolic leaves in a closed 3-manifold $M$ whose fundamental group is not solvable, and let $\mathcal{G}$ be the one dimensional foliation obtained by inte
Externí odkaz:
http://arxiv.org/abs/2310.05176
Autor:
Fenley, Sergio R., Potrie, Rafael
We show that if $\mathcal{F}_1$ and $\mathcal{F}_2$ are two transverse minimal foliations on $M = T^1S$ then either they intersect in an Anosov foliation or there exists a Reeb-surface in the intersection foliation. The existence of a Reeb surface is
Externí odkaz:
http://arxiv.org/abs/2303.14525
We give a geometric characterization of the quantitative non-integrability, introduced by Katz, of strong stable and unstable bundles of partially hyperbolic measures and sets in dimension 3. This is done via the use of higher order templates for the
Externí odkaz:
http://arxiv.org/abs/2302.12981
Autor:
Fenley, Sergio R., Potrie, Rafael
We consider a class of partially hyperbolic diffeomorphisms introduced in [BFP] which is open and closed and contains all known examples. If in addition the diffeomorphism is non-wandering, then we show it is accessible unless it contains a su-torus.
Externí odkaz:
http://arxiv.org/abs/2103.14630
Autor:
Potrie, Rafael
For every $\mathcal{U} \subset \mathrm{Diff}^\infty_{vol}(\mathbb{T}^2)$ there is a measure of finite support contained in $\mathcal{U}$ which is uniformly expanding.
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/2103.02364
Autor:
Fenley, Sergio R., Potrie, Rafael
We show that if a hyperbolic 3-manifold admits a partially hyperbolic diffeomorphism then it also admits an Anosov flow. Moreover, we give a complete classification of partially hyperbolic diffeomorphism in hyperbolic 3-manifolds as well as partially
Externí odkaz:
http://arxiv.org/abs/2102.02156
We propose a generalization of the concept of discretized Anosov flows that covers a wide class of partially hyperbolic diffeomorphisms in 3-manifolds, and that we call collapsed Anosov flows. They are related with Anosov flows via a self orbit equiv
Externí odkaz:
http://arxiv.org/abs/2008.06547
Publikováno v:
Geom. Topol. 27 (2023) 3095-3181
We study $3$-dimensional partially hyperbolic diffeomorphisms that are homotopic to the identity, focusing on the geometry and dynamics of Burago and Ivanov's center stable and center unstable \emph{branching} foliations. This extends our study of th
Externí odkaz:
http://arxiv.org/abs/2008.04871
Autor:
Potrie, Rafael
This is an expository note intended to illustrate current research in topological study of partially hyperbolic diffeomorphisms in dimension 3 with a beautiful result due to Margulis and Plante-Thurston on topological obstructions for a manifold to a
Externí odkaz:
http://arxiv.org/abs/2005.10889