Smooth dynamics via Operators, with Singularities

ERC AdG SOS (2018-2023)

Transfer operators applied to hyperbolic systems with low regularity including billiards

(rates of mixing, linear or fractional response Ruelle resonances, susceptibility function etc.)

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This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 787304)

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The Research Group:

Viviane BALADI (PI)

Postdocs:

• Juho LEPPÄNEN
  Oct 2018-January 2020
  Central limit theorems with a rate of convergence for time-dependent intermittent maps (with Olli Hella) Stochastics and Dynamics, doi.org/10.1142/S0219493720500215
  Sunklodas' approach to normal approximation for time-dependent dynamical systems (with Mikko Stenlund) submitted
  On the fractional susceptibility function of piecewise expanding maps, (with M. Aspenberg, J. Leppänen, T. Persson), submitted
  
  
• Fanni SELLEY, 16-26/129 (in the nook 16-26/117-127)
  Oct 2019-Sep 2021
  A self-consistent dynamical system with multiple absolutely continuous invariant measures, submitted
  Linear Response for a Family of Self-Consistent Transfer Operators, (with Matteo Tanzi), submitted
  
  
• Julien SEDRO, 16-26/129 (in the nook 16-26/117-127)
  Oct 2019-Sep 2021
  Arnold maps with noise: Differentiability and non-monotonicity of the rotation number (with S. Galatolo, A. Di Garbo, M. Ghil) to appear J Stat Phys, DOI:10.1007/s10955-019-02421-1
  Quadratic response of random and deterministic dynamical systems (with Stefano Galatolo), Chaos 30, 023113 (2020); DOI:10.1063/1.5122658
  Regularity of characteristic exponents and linear response for transfer operator cocycles (with H.H. Rugh), submitted
  
  
• Caroline WORMELL
  Dec 2020-Nov 2022
  
  
• Roberto CASTORRINI
  Dec 2020-Nov 2021 and Dec 2021-Nov 2022
  
  
• Jungwon LEE External funding, 16-26/129 (in the nook 16-26/117-127)
  Sep 29, 2019 - Dec 1, 2019/Dec 13, 2019/ Jan 17, 2010 - Feb 14, 2020 /March 2020-Aug 2021
  

PhD students:


• Alexander ADAM (external funding)
  Horocycle averages on closed manifolds and transfer operators
  
  
• Malo JÉZÉQUEL 16-26/131
  Sep 2018-Aug 2021
  Local and global trace formulae for smooth hyperbolic diffeomorphisms, J. Spectr. Theory, 10 (2020), 185-249, DOI: 10.4171/JST/290.
  Global trace formula for ultra-differentiable Anosov flows Submitted
  Transfer operator for ultradifferentiable expanding maps of the circle, to appear ETDS
  FBI Transform in Gevrey Classes and Anosov Flows with Y. Guedes Bonthonneau
  
  
• Jérôme CARRAND
  Sep 2020-Aug 2023.
  
  

Publications of the PI:
There are no deviations for the ergodic averages of the Giulietti--Liverani horocycle flows on the two-torus, to appear ETDS
On the measure of maximal entropy for finite horizon Sinai billiard maps (with M. Demers) arxiv, JAMS (2020), DOI: https://doi.org/10.1090/jams/939
On the fractional susceptibility function of piecewise expanding maps, (with M. Aspenberg, J. Leppänen, T. Persson), submitted

Visitors:
Daniel SMANIA (November-December 2018). Talk November 30, 14:00, Dynamics seminar in Jussieu. "Transfer operators and atomic decomposition"
Alexander ADAM, Oscar BANDTLOW, Carlangelo LIVERANI, Frédéric NAUD, Mark POLLICOTT, Barbara SCHAPIRA (December 2018, Several talks at Journées dynamiques, Sophie Germain, Dec 6-8, 2018).
Alexey KOREPANOV, March 30-April 3, 2019 (Ergodic theory seminar April 2)
Thomas OHLSON TIMOUDAS, week of June 17, 2019 (Ergodic theory seminar June 18, 2019)
Mike TODD, week of June 24, 2019. (Ergodic theory seminar June 25, 2019)
Daniel SMANIA, Alexei KOREPANOV, Mike TODD, Benoit SAUSSOl, J WOUTERS, Caroline WORMELL, Dima DOLGOPYAT: Oct 13-18, 2019 (Workshop at IhP)
Anke POHL, November 4-7, 2019. (Seminar Topology and Geometries, Nov 7, 2019)


Events (co-)organised:

Dec 6-8, 2018, Journées de dynamique, Paris (Co-organised)

Oct 14-16, 2019, Workshop on Response Theory and Its Applications in Geophysical Fluid Dynamics, (coorganised with Bahsoun, Galatolo, and Lucarini) IHP, CliMath

January 4, 2021-June 30, 2021: Dynamics, Transfer Operators, and Spectra, Semester at Centre Interfacultaire Bernoulli, Ecole Polytechnique Fédérale de Lausanne (Co-organised) Semester page

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Timeline:

September 3-5, 2018, Dynamics Days Europe, Loughborough

Oct 29-Nov 2, 2018, Probabilistic limit theorems for dynamical systems, CIRM Luminy

Dec 6-8, 2018, Journées de dynamique, Paris (Co-organised)

Jan 28, 2019: Seminar, Rennes

Feb 5-8, 2019: Roma Tor Vergata, Workshop "Dynamical Systems: From Geometry to Mechanics"

March 26, 2019, Amiens Journée dynamique

April 6 -May 1, 2019: Sao Carlos, USP, Brazil (visiting D. Smania)

May 12-18, 2019: Luminy, Beyond Hyperbolicity

June 9-15, 2019: Oberwolfach Seminar, Anisotropic Spaces and Applications to Hyperbolic and Parabolic Dynamical Systems, MFO

July 1-5, 2019: Thermodynamic Formalism: Modern Techniques in Smooth Ergodic Theory , CIRM, Luminy

July 7-11, 2019: Oberwolfach, Dynamische Systeme

July 22-26, 2019, Thermodynamic Formalism: Ergodic Theory and Geometry Warwick

September 16-20, 2019, Kraków, Dynamics, Equations and Applications (DEA 2019)

Oct 14-16, 2019, Workshop on Response Theory and Its Applications in Geophysical Fluid Dynamics, (coorganised with Bahsoun, Galatolo, and Lucarini) IHP, CliMath

Dec 2-6, 2019 Low-dimensional and Complex Dynamics, CIB-EPFL Lausanne.

Jan 20-23, 2020, Statistical aspects of geodesic flows in nonpositive curvature, Warwick

Feb 2-7, 2020, Transfer operators in number theory and quantum chaos - HIM Bonn

March 8-15, 2020, University of Vienna, Austria

January 10, 2021-June 30, 2021: Dynamics, Transfer Operators, and Spectra, Semester at Centre Interfacultaire Bernoulli, Ecole Polytechnique Fédérale de Lausanne (3-4 months in Lausanne)

June 7-10, 2021: Geneva, JPE 77

June 28-July 2, 2021, minicourse at JISD 2021, CIRM, Barcelona

August 2-7, 2021: ICMP, Geneva

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