scholarly journals Partial hyperbolicity and foliations in $\mathbb{T}^3$

2015 ◽  
Vol 9 (01) ◽  
pp. 81-121 ◽  
Author(s):  
Rafael Potrie ◽  
Keyword(s):  
Partial Hyperbolicity

Studying partial hyperbolicity inside regimes of motion in Hamiltonian systems

2021 ◽  
Vol 144 ◽  
pp. 110640
Author(s):  
Miguel A. Prado Reynoso ◽  
Rafael M. da Silva ◽  
Marcus W. Beims
Keyword(s):  
Hamiltonian Systems ◽  
Partial Hyperbolicity

scholarly journals Partial hyperbolicity and classification: a survey

2016 ◽  
Vol 38 (2) ◽  
pp. 401-443 ◽  
Author(s):  
ANDY HAMMERLINDL ◽  
RAFAEL POTRIE
Keyword(s):  
Fundamental Group ◽  
Three Dimensional ◽  
Group Classification ◽  
Partial Hyperbolicity ◽  
Hyperbolic Diffeomorphisms ◽  
Higher Dimensional ◽  
Partially Hyperbolic ◽  
Anosov Flows ◽  
Partially Hyperbolic Diffeomorphisms ◽  
Solvable Fundamental Group

This paper surveys recent results on classifying partially hyperbolic diffeomorphisms. This includes the construction of branching foliations and leaf conjugacies on three-dimensional manifolds with solvable fundamental group. Classification results in higher-dimensional settings are also discussed. The paper concludes with an overview of the construction of new partially hyperbolic examples derived from Anosov flows.

scholarly journals Volume hyperbolicity and wildness

2016 ◽  
Vol 38 (3) ◽  
pp. 886-920
Author(s):  
CHRISTIAN BONATTI ◽  
KATSUTOSHI SHINOHARA
Keyword(s):  
Main Tool ◽  
Periodic Points ◽  
Necessary Condition ◽  
Partial Hyperbolicity ◽  
Chain Recurrence ◽  
Markov Partitions ◽  
Open Set ◽  
Partially Hyperbolic ◽  
Uniform Expansion

It is known that volume hyperbolicity (partial hyperbolicity and uniform expansion or contraction of the volume in the extremal bundles) is a necessary condition for robust transitivity or robust chain recurrence and hence for tameness. In this paper, on any $3$-manifold we build examples of quasi-attractors which are volume hyperbolic and wild at the same time. As a main corollary, we see that, for any closed $3$-manifold $M$, the space $\text{Diff}^{1}(M)$ admits a non-empty open set where every $C^{1}$-generic diffeomorphism has no attractors or repellers. The main tool of our construction is the notion of flexible periodic points introduced in the authors’ previous paper. In order to eject the flexible points from the quasi-attractor, we control the topology of the quasi-attractor using the notion of partially hyperbolic filtrating Markov partitions, which we introduce in this paper.

scholarly journals Entropic stability beyond partial hyperbolicity

2013 ◽  
Vol 7 (4) ◽  
pp. 527-552 ◽  
Author(s):  
Jérôme Buzzi ◽  
◽  
Todd Fisher ◽  
Keyword(s):  
Partial Hyperbolicity

scholarly journals Partial hyperbolicity and ergodicity in dimension three

2008 ◽  
Vol 2 (2) ◽  
pp. 187-208 ◽  
Author(s):  
Federico Rodriguez Hertz ◽  
◽  
María Alejandra Rodriguez Hertz ◽  
Raúl Ures ◽  
Keyword(s):  
Partial Hyperbolicity

scholarly journals Partial hyperbolicity of G-induced flows.

1989 ◽  
Vol 23 (1) ◽  
pp. 475-479 ◽  
Author(s):  
M. L. Chumak ◽  
A. M. Stepin
Keyword(s):  
Partial Hyperbolicity
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