Smooth dynamics via Operators, with Singularities

ERC AdG SOS (September 2018-December 2023, 64 months)

Transfer operators applied to hyperbolic systems with low regularity including billiards

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

---

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)

---

Previous job openings here


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, V. Baladi, T. Persson), DCDS 42 (2022) 679-706
  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
  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) Nonlinearity, 35, 3991-4042 (2022) DOI 10.1088/1361-6544/ac640f
  Map lattices coupled by collisions: hitting time statistics and collisions per lattice unit (with W .Bahsoun) Ann. Henri Poincaré, 23, 2919-2947 (2022)https://doi.org/10.1007/s00023-022-01164-2
  Synchronization for Networks of Globally Coupled Maps in the Thermodynamic Limit (with M. Tanzi) J. Stat. Phys, 189, 16 (2022) https://doi.org/10.1007/s10955-022-02968-6
  
  
• Julien SEDRO, 16-26/129
  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), ETDS, https://doi.org/10.1017/etds.2021.153
  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), Stochastics and Dynamics, 23, 2350046 (2023) https://doi.org/10.1142/S0219493723500466
  A vector-valued almost sure invariance principle for random expanding on average cocycles, (with D. Dragicevic and Y. Hafouta), J. Stat. Phys. 190, 54 (2023) https://doi.org/10.1007/s10955-023-03067-w
  Quenched linear response for smooth expanding on average cocycles, (with D. Dragicevic and P. Giulietti) Comm. Math. Phys., 399, 423-452 (2023) DOI:10.1007/s00220-022-04560-1
  
  
  
• Caroline WORMELL, 16-26/129
  Jan 2021-Dec 2022
  Efficient computation of statistical properties of intermittent dynamics , arXiv 2021
  Non-hyperbolicity in large-scale dynamics of a chaotic system, Proceedings of the Royal Society A 478 Issue 2261 (2022) https://doi.org/10.1098/rspa.2021.0808
  Conditional mixing in deterministic chaos Ergodic Theory and Dynamical Systems , First View (2024) https://doi.org/10.1017/etds.2023.55
  On convergence of linear response formulae in some piecewise hyperbolic maps arXiv 2022, submitted
  
  
• Roberto CASTORRINI, 16-26/129
  Dec 2020-January 2022
  Quantitative statistical properties of two-dimensional partially hyperbolic systems (with C. Liverani), Advances in Mathematics 409 (2022) doi.org/10.1016/j.aim.2022.108625
  Thermodynamic formalism for piecewise expanding maps in finite dimension (with V. Baladi), arXiv and HAL, DCDS (2024) doi:10.3934/dcds.2024023
  
  
• Alexey KOREPANOV, 16-26/129
  April 2021-September 2022
  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
  Rates of mixing for the measure of maximal entropy of dispersing billiard maps (with M. Demers) Proc. London Math Soc., 128 (2024) https://doi.org/10.1112/plms.12578
  
  
• Jungwon LEE External funding, 16-26/129
  Sep 29, 2019 - Dec 1, 2019/Dec 13, 2019/ Jan 17, 2020 - 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), Tunisian J. Math 4 387-441 (2022) doi:10.2140/tunis.2022.4.387
  
  
• 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, to appear Astérisque
  Semiclassical measures for higher dimensional quantum cat maps with S. Dyatlov, Ann. Henri Poincaré (2023). https://doi.org/10.1007/s00023-023-01309-x
  Rigorous justification for the space-split sensitivity algorithm to compute linear response in Anosov systems with N. Chandramoorthy, Nonlinearity 35 4357-4391 (2022) DOI: https://doi.org/10.1088/1361-6544/ac7692
  Scattering rigidity for analytic metrics with Y. Guedes Bonthonneau and C. Guillarmou, Cambridge J. Math. 12 165-222 (2024) DOI: https://dx.doi.org/10.4310/CJM.2024.v12.n1.a2
  
  
• Jérôme CARRAND 16-26/131
  Sep 2020-Aug 2023.
  Measure of maximal entropy for finite horizon Sinai billiard flows (with V. Baladi and M. Demers) (2022) arXiv and HAL, to appear Ann. H. Lebesgue
  A family of natural equilibrium measures for Sinai billiard flows to appear Ann IHP Proba Stat
  Logarithmic bounds for ergodic sums of certain flows on the torus: a short proof, Qual. Theory Dyn. Syst. 21 issue 3, pp ?? (2022) doi.org/10.1007/s12346-022-00632-8
  Smooth generalized interval exchange transformations with wandering intervals, from explicit derived from pseudo-Anosov maps, Nonlinearity 36 476-506 (2023) doi.org/10.1088/1361-6544/aca5e0
  
  

Publications of the PI:
Thermodynamic formalism for piecewise expanding maps in finite dimension (with R. Castorrini), arXiv and HAL, DCDS (2024), doi:10.3934/dcds.2024023
A parameter ASIP for the quadratic family (with M. Aspenberg and T. Persson) arXiv and HAL, submitted
Measure of maximal entropy for finite horizon Sinai billiard flows (with J. Carrand and M. Demers) (2022) arXiv and HAL, to appear Ann. H. Lebesgue
Thermodynamic formalism for dispersing billiards (with M. Demers) J. Mod. Dynam. 18 415-493 (2022) 10.3934/jmd.2022013
There are no deviations for the ergodic averages of the Giulietti--Liverani horocycle flows on the two-torus, ETDS 42 Anatole Katok Memorial Issue Part 1 (2022) 500-513, 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 42 (2022) 679-706, 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), Tunisian J. Math 4 387-441 (2022) doi:10.2140/tunis.2022.4.387

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)
Roberto CASTORRINI, March 27-31, 2022. Feb 6-10, 2023.


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-January 24, 2022: Working group, - Monday 14:00-16:00

---

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

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

Sept 8-9, 2022, Heilbronn IMR Annual Conference, Bristol

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

19-23 December 2022: The Lorentz gas at the intersection of smooth ergodic theory and probability theory. Lorentz Center, Leiden.

March 6-18, 2023: Two dimensional maps, Institut Mittag Leffler, Sweden

3-5 July 2023, Summer school CRM Barcelona (School on Interaction between Dynamical Systems and Partial Differential Equations JISD2023)

July 7 2023, Ecole d'été de l'IMJ-PRG (Jussieu)

July 16-21, 2023, Thermodynamic Formalism for Geodesic Flows, BIRS-UBCO, University British Columbia Okanagan, Kelowna, Canada. (online)

---