Fast-Slow Partially Hyperbolic Systems

Fast-Slow Partially Hyperbolic Systems

July 2026
Jilin University

Schedule

Starting: 24 July, 2026.
End: 31 July 2026.
Six lectures of 1:30 each.

Here are some notes (for the students' eyes only) that I hope may help. In particular, the appendices contain all the functional analysis needed to follow the course.

  • An idiosyncratic introduction to Dynamical Systems. These are notes (in a draft form, read at your own risk) intended for people with little or no knowledge of dynamical systems; the relevant part for this course starts from chapter 7. Moreover, the Appendices A, C, D, F and H may be useful.

    More information on transfer operators can be found in the following books:

  • Transfer operators in Hyperbolic Dynamics An introduction, C.Liverani, M. Demers and N. Kiamari. 33 Colloquio Brasilero de Matematica. Editora do IMPA. pp.252 (2021)
  • V. Baladi. Positive Transfer Operators and Decay of Correlations. Advanced Series in Nonlinear Dynamics: Volume 16 (2000) https://doi.org/10.1142/3657
  • Boyarsky, Abraham; Gò ra, Pawel Laws of chaos. Invariant measures and dynamical systems in one dimension. Probab. Appl.Birkhauser Boston, Inc., Boston, MA, (1997).

    The first is partially a review, so some topics are not treated in full detail. The second is much more detailed, although it covers less material. The third is a bit dated and covers only one-dimensional maps, but it contains some nice facts.

    Here are some articles that contain material relevant to the course: this is the article that started my itnerest on fast-slow systems and this cotains some physical motivations; this is a simple explanation of Dolgopyat's martignale method; these are three papers that contain the main results limit theorems, statistical properties and general assessment of the state of the art; this is an approach based on transfer operators; finally, this is a new result.

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