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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 ...
RegularGraph's user avatar
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 ...
Ali Taghavi's user avatar
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) \...
Adam's user avatar
  • 1,043
1 vote
0 answers
93 views

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 $(...
D. Ford's user avatar
  • 151
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 ...
Pietro Majer's user avatar
  • 60.6k
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 ...
Michal's user avatar
  • 199
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^...
mac's user avatar
  • 279
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,...
Olga's user avatar
  • 1,143
1 vote
2 answers
433 views

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 ...
Pengfei's user avatar
  • 2,244