Compact locally maximal hyperbolic sets for smooth maps: fine statistical properties

By S. Gouëzel, C. Liverani. 2006

132 citations recorded by the source corpus.

Compact locally maximal hyperbolic sets are studied via geometrically defined functional spaces that take advantage of the smoothness of the map in a neighborhood of the hyperbolic set. This provides a self-contained theory that not only reproduces all the known classical results, but also gives new insights on the statistical properties of these systems.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6d433abb93914a86d7bc477a5de60ca231c3fdb3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. M. Tsujii
2. Viviane Baladi
3. F. Faure
4. Oliver Butterley
5. C. Liverani

In Mathematical Physics

1. Viviane Baladi
2. M. Tsujii
3. Oliver Butterley
4. C. Liverani
5. Mark Pollicott
6. P. Giulietti
7. F. Faure
8. David Ruelle

Citations in the corpus

• Anosov flows and dynamical zeta functions (2012, background): “Accordingly, all the present arguments can be repeated in complete analogy, although one must compute in the more sophisticated way detailed in [20].”
• Decay of correlations in suspension semi-flows of angle-multiplying maps (2005, background): “For the cases of discrete dynamical systems such as iterations of expanding maps and Anosov diffeomorphisms, exponential decay of correlations for Hölder observables was already known in the early stage of the study [6, 16, 17] and nowadays we have a fairly good understanding of the speed of decay a”
• Smooth Anosov flows: Correlation spectra and stability (2007, background): “The recent papers [19, 18, 12, 2, 3, 20, 9, 7, 21, 4, 13 ], have shown that such an approach yields a simpler and far reaching alternative to the more traditional point of view based on Markov partitions.”
• The semiclassical zeta function for geodesic flows on negatively curved manifolds (2013, methodology): “To avoid this difficulty, we actually consider the corresponding transfer operators on a Grassmann bundle G over the manifold M (In the literature, this kind of idea is found in the papers [7,24]).”
• Linear response, or else (2014, background): “The result and proof are well known (and simpler than the analogous arguments in [24, 9]), but we are not aware of any reference.”