All Questions
Tagged with foliations hyperbolic-dynamics
9 questions
8
votes
1
answer
718
views
A concept of dynamical coherence
I'm trying to make an overview of the study of partial hyperbolicity and there is an interesting concept of dynamical coherence which appears there. Some call it mild (see the Thesis of Pablo Carrasco,...
- 1,143
4
votes
1
answer
246
views
Lipschitz property of holonomies fails when stable leaves $W^s(x)$ inside the leaves $W^{ss}(x)$
Let $M$ be compact manifold. suppose $f:M\rightarrow M$ is $C^{2}$.
There is a continuous splitting of the tangent bundle $TM=E^{ss}+E^{s}+E^{u}$ invariant under the derivative $Df$ of the ...
- 199
4
votes
0
answers
101
views
Terminology for a foliation that is only tangentially smooth
I'd like to get some information and references, starting with a name, for the following quite common situation, for a smooth (i.e. $C^\infty$) $n$-manifold $M$. A partition $\mathcal{L}$ of $M$ is ...
- 60.6k
3
votes
1
answer
81
views
Can the Reeb foliation of $S^3$ be realized as stable manifold foliation of a smooth hyperbolic discrete dynamic on $S^3$?
Can the Reeb foliation of $S^3$ be realized as foliation associated to stable(or unstable) manifolds of a hyperbolic discrete dynamic on $S^3$?If yes what is a precise formulation for that ...
- 366
2
votes
1
answer
283
views
the union of local stable manifolds along local unstable manifolds
Let $f:M\rightarrow M$ be a $C^2$ hyperbolic diffeomorphism on compact connected riemannian manifold $M$. then there are local stable and unstable manifolds at each point denoted by $W^s_\delta(x), W^...
- 279
1
vote
1
answer
148
views
Non-absolutely continuous foliation
What is a simple example of a (continuous) foliation of a manifold that is not absolutely continuous?
(A foliation is said to be absolutely continuous if holonomy maps between smooth transversals send ...
- 133
1
vote
2
answers
433
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Extension of integrable distribution over a subset
Let $M$ be a smooth manifold and $G_k(M)$ be the $k$-dimensional Grassmian bundle of $M$. Let $K\subset M$ be a compact subset and $E:K\to G_k(M)$ be a continuous distribution on $K$.
We say $E$ is ...
- 2,244
1
vote
0
answers
93
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Transverse measures in pseudo-Anosov diffeomorphisms
I've recently begun doing research involving pseudo-Anosov diffeomorphisms, which are diffeomorphisms on surfaces $f : M \to M$ admitting two singular measured foliations $(\mathcal F^s, \nu^s)$ and $(...
- 151
0
votes
0
answers
61
views
Unique poine in holonomies
Let $\Lambda$ be Axiom A for $C^{1+\gamma}$ $f$. I am reading this paper. I have a problem to undestand holonomies. The holonomy mapping
$$ h: W_{loc}^{s} (x) \cap\Lambda \rightarrow W_{loc}^{s} (y) \...
- 1,043