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SOS SIGNED

Smooth dynamics via Operators, with Singularities

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Project "SOS" data sheet

The following table provides information about the project.

Coordinator
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS 

Organization address
address: RUE MICHEL ANGE 3
city: PARIS
postcode: 75794
website: www.cnrs.fr

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
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fax: n.a.

 Coordinator Country France [FR]
 Total cost 1˙830˙070 €
 EC max contribution 1˙830˙070 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2017-ADG
 Funding Scheme ERC-ADG
 Starting year 2018
 Duration (year-month-day) from 2018-09-01   to  2023-08-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS FR (PARIS) coordinator 1˙830˙070.00

Map

 Project objective

The ergodic theory of smooth dynamical systems enjoying some form of hyperbolicity has undergone important progress since the beginning of the twenty first century, in part due to the development of a new technical tool: anisotropic Banach or Hilbert spaces, on which transfer operators have good spectral properties. Very recently, such tools have yielded exponential mixing for dispersing (Sinai) billiard flows (i.e. the 2D periodic Lorentz gas), which are the archetypal smooth systems with singularities.

We will study other challenging natural systems, mostly with singularities, by using functional analytical tools, in particular transfer operators acting on anisotropic spaces (including the new 'ultimate' space introduced recently, which combines desirable features of several existing spaces), and revisiting the Milnor-Thurston kneading theory to obtain nuclear decompositions in low regularity.

Goals of the project include:

-Thermodynamic formalism for the Sinai billiard maps and flows (2D periodic Lorentz gas), in particular existence and statistical properties of the measure of maximal entropy.

-Intrinsic resonances of Sinai billiard maps and flows (2D periodic Lorentz gas) via the dynamical zeta function.

-Fine statistical properties of (infinite measure) semi-dispersing billiards with non compact cusps.

-Growth of dynamical determinants and zeta functions of differentiable (non analytic) geodesic flows, with applications to the global Gutzwiller formula.

-Fractional response and fractional susceptibility function for transversal families of smooth nonuniformly hyperbolic maps (including the logistic family).

 Publications

year authors and title journal last update
List of publications.
2020 Viviane Baladi, Mark F. Demers
On the measure of maximal entropy for finite horizon Sinai Billiard maps
published pages: 381-449, ISSN: 0894-0347, DOI: 10.1090/jams/939
Journal of the American Mathematical Society 33/2 2020-04-15
2019 Olli Hella, Juho Leppänen
Central limit theorems with a rate of convergence for time-dependent intermittent maps
published pages: 2050025, ISSN: 0219-4937, DOI: 10.1142/S0219493720500252
Stochastics and Dynamics 2019 2020-04-15
2020 Stefano Galatolo, Julien Sedro
Quadratic response of random and deterministic dynamical systems
published pages: 23113, ISSN: 1054-1500, DOI: 10.1063/1.5122658
Chaos: An Interdisciplinary Journal of Nonlinear Science 30/2 2020-04-15

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