Stable ergodicity of certain linear automorphisms of the torus
By F. R. Hertz. 2002
64 citations recorded by the source corpus.
We find a class of ergodic linear automorphisms of TN that are stably ergodic. This class includes all non-Anosov ergodic automorphisms when N = 4. As a corollary, we obtain the fact that all ergodic linear automorphism of TN are stably ergodic when N iU 5.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/cdcba7820806ed8d8c11606c6719a0f78cdfdbdf
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
- Artur Avila
- Marcelo Viana
- Danijela Damjanović
- A. Katok
- A. Zorich
- Jiagang Yang
- Alexander I. Bufetov
- Corentin Boissy
In Mathematical Physics
- Artur Avila
- Marcelo Viana
- Danijela Damjanović
- A. Katok
- Jiagang Yang
- A. Zorich
- F. R. Hertz
- Amie Wilkinson
Citations in the corpus
- On the regularization of conservative maps (2008, background): “and for most results on stable ergodicity such as [12], though more regularity is necessary if KAM methods are involved [ 23 ]).”
- Extremal Lyapunov exponents: an invariance principle and applications (2010, methodology): “Then by Rodriguez-Hertz [26], the strong stable and strong unstable subbundles are jointly integrable and, in fact, the su-foliation of f is smoothly conjugate to the su-foliation of A.”
- Local rigidity of partially hyperbolic actions I. KAM method and ${\mathbb Z^k}$ actions on the torus (2010, background): “The existence of genuinely partially hyperbolic irreducible actions in any odd dimension is ruled out by the fact that any A ∈ SL(N,Z) with irreducible characteristic polynomial and N odd, is hyperbolic [33].”