Questions tagged [partial-hyperbolicity]

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$C^1$ partially hyperbolic diffeomorphism have Hölder stable holonomies (reference request)

I have spent an insane amount of time searching for a preprint I have printed a few months ago but misplaced. I cannot find it anymore and this drives me crazy. It might not have been meant for ...
5
votes
2answers
834 views

Eigenvalues of the D'Alembertian operator

My question about the spectral theory of the D'Alembertian operator on a Lorentzian manifolds (say the spacetime $M^{3+1}$) given by $$\square = -\partial_{t}^2 + \Delta$$ for the metric $g=(-+++)$. ...
6
votes
1answer
180 views

Is there a similar theorem in the partially hyperbolic case?

Theorem 5.10.3 from Introduction to dynamical systems, by Brin & Stuck: Let $f:M\rightarrow M$ be an Anosov diffeomorphism. Then the following are equivalent: $NW(f)=M$, every unstable manifold ...
2
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1answer
444 views

Center-stable manifolds

Let $f:M\to M$ be a partially hyperbolic diffeomorphism. That is, there exists a continuous splitting $TM=E^u\oplus E^c\oplus E^s$ into unstable, center and stable bundles. It is well known that there ...