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)
-
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), arXiv 2021, submitted
A vector-valued almost sure invariance principle for
random expanding on average cocycles,
(with D. Dragicevic and Y. Hafouta), J. Stat. Phys. (2023)
Quenched linear response for smooth expanding on average cocycles,
(with D. Dragicevic and P. Giulietti), arxiv 2021, submitted
-
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
arXiv 2022, to appear Ergodic Theory and Dynamical Systems
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, submitted
- 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), arXiv 2022, submitted
- 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, 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 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
- 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
A family of natural equilibrium
measures for Sinai billiard flows
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, submitted
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, submited
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)
Viviane Baladi