Smooth dynamics via Operators, with Singularities

ERC AdG SOS (September 2018-February 2024, 66 months)

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) J. Stat. Phys. 181 (2020) 1523-1564, doi.org/10.1007/s10955-020-02636-7
  On the fractional susceptibility function of piecewise expanding maps, (with M. Aspenberg, J. Leppänen, T. Persson), submitted
  Loss of memory and moment bounds for nonstationary intermittent dynamical systems, (with A. Korepanov), Comm Math Phys 385 (2021) 905-935 , doi.org/10.1007/s00220-021-04071-5
  
• 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, J. Comput. Dynam. 8 (2021) 9-32; doi:10.3934/jcd.2021002
  Linear Response for a Family of Self-Consistent Transfer Operators, (with Matteo Tanzi), Comm. Math. Phys. 382, 1601-1624 (2021) doi.org/10.1007/s00220-021-03983-6
  Conditioning problems for invariant sets of expanding piecewise affine mappings: Application to loss of ergodicity in globally coupled maps, (with B. Fernandez)
  Map lattices coupled by collisions: hitting time statistics and collisions per lattice unit (with W .Bahsoun)
  Synchronization for Networks of Globally Coupled Maps in the Thermodynamic Limit (with M. Tanzi)
  
  
• Julien SEDRO, 16-26/129 (in the nook 16-26/117-127)
  Oct 2019-Sep 2021
  Oct 2021-Sep 2022 (external funding)
  Arnold maps with noise: Differentiability and non-monotonicity of the rotation number (with S. Galatolo, A. Di Garbo, M. Ghil) J Stat Phys, 179 (2020) 1594-1624, https://doi.org/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), Comm Math Phys, 383 (2021) 1243-1289, https://doi.org/10.1007/s00220-021-04019-9
  Statistical stability and linear response for random hyperbolic dynamics (with D. Dragicevic), arXiv 2020, to appear ETDS
  Pre-threshold fractional susceptibility functions at Misiurewicz parameters, Nonlinearity 34 (2021) 7174-7184, https://doi.org/10.1088/1361-6544/ac20a3
  Quenched limit theorems for expanding on average cocycles (with D. Dragicevic), arXiv 2021, submitted
  A vector-valued almost sure invariance principle for random expanding on average cocycles, (with Davor Dragicevic and Yeor Hafouta), arXiv 2021, submitted
  
  
• Caroline WORMELL, 16-26/129 (in the nook 16-26/117-127)
  Jan 2021-Dec 2022
  Efficient computation of statistical properties of intermittent dynamics , arXiv 2021
  Non-hyperbolicity in large-scale dynamics of a chaotic system, arXiv 2021
  
  
• Roberto CASTORRINI, 16-26/129 (in the nook 16-26/117-127)
  Dec 2020-April 2022
  May 2022-Nov 2022 (external funding)
  Quantitative statistical properties of two-dimensional partially hyperbolic systems (with C. Liverani), arXiv 2020, submitted
  
  
• Alexey KOREPANOV, 16-26/129
  April 2021-March 2023
  Loss of memory and moment bounds for nonstationary intermittent dynamical systems, (with J. Leppanen), Comm Math Phys 385 (2021) 905-935 , doi.org/10.1007/s00220-021-04071-5
  
  
• 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, until Sept 2020)
  Horocycle averages on closed manifolds and transfer operators (v3 with V. Baladi), arXiv 2021, submitted
  
  
• 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 Comm Math Phys, 385, 1771-1834 (2021) doi.org/10.1007/s00220-020-03930-x
  Transfer operator for ultradifferentiable expanding maps of the circle, Ergodic Th Dyn Sys, 41 , 2049-2068 (2021) DOI: https://doi.org/10.1017/etds.2020.36
  FBI Transform in Gevrey Classes and Anosov Flows with Y. Guedes Bonthonneau, submitted
  Semiclassical measures for higher dimensional quantum cat maps with S. Dytalov
  Rigorous justification for the space-split sensitivity algorithm to compute linear response in Anosov systems with Nisha Chandramoorthy
  
  
• Jérôme CARRAND 16-26/131
  Sep 2020-Aug 2023.
  Logarithmic bounds for ergodic averages of constant type rotation number flows on the torus: a short proof, submitted
  Explicit construction of non-linear pseudo-Anosov maps, with nonminimal invariant foliations, submitted
  
  

Publications of the PI:
Thermodynamic formalism for dispersing billiards (with M. Demers) (2020) arXiv and Hal, submitted
There are no deviations for the ergodic averages of the Giulietti--Liverani horocycle flows on the two-torus, ETDS online (2021) DOI: https://doi.org/10.1017/etds.2021.17
On the measure of maximal entropy for finite horizon Sinai billiard maps (with M. Demers) JAMS 33 381-449 (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), DCDS (2021) doi:10.3934/dcds.2021133
Fractional susceptibility functions for the quadratic family: Misiurewicz-Thurston parameters (with D Smania), Comm. Math. Phys. 385 1957-2007 (2021) https://doi.org/10.1007/s00220-021-04015-z
Horocycle averages on closed manifolds and transfer operators (with A. Adam), arXiv and Hal, submitted, 2021

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 25, 2021-March 26, 2021: Dynamics, Transfer Operators, and Spectra, Semester at Centre Interfacultaire Bernoulli, Ecole Polytechnique Fédérale de Lausanne (Co-organised) Semester page

February 19-April 16, 2021: Ruelle-Pollicott Resonances in dynamics and semiclassical analysis, - Friday 10:00-12:00 - BigBlueButton

September 20, 2021-March 28, 2022: Working group, - Monday 14:00-16:00

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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 (online)

June 7, 11, 2021: Mittag-Leffler, Sweden, New frontiers in dimension theory of dynamical systems - Applications in metric number theory (online)

June 21-25, 2021 Ecole d'été finistérienne en systèmes dynamiques

July 11-18, 2021, Oberwolfach, Dynamische Systeme

August 1-3, 2021: ICMP, Geneva

Nov 8-10, 2021, Nantes, Meeting G Rivière

February 11, 2022, "One World Dynamics" seminar (session on multiscale dynamics) online

March 7-11, 2022, Roscoff? (TBC)

June 6-10, 2022: Limit Theorems for Slowly Mixing Systems, Edinburgh

July 5-9, 2022, "Global and local aspects in dynamical systems: From Exponentially small phenomena to Instability" (GLADS21), Barcelona

Oct 3-7, 2022: Luminy CIRM, Probabilistic techniques for random and time-dependent dynamical systems

July 2023 (TBC), Summer school CRM Barcelona (School on Interaction between Dynamical Systems and Partial Differential Equations JISD20213)

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