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IChaos SIGNED

Intermediate Chaos

Total Cost €

EC-Contrib. €

Partnership

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Outcomes and
results

IChaos project word cloud

Explore the words cloud of the IChaos project. It provides you a very rough idea of what is the project "IChaos" about.

pi central asymptotic genus orthogonally entropy decades avenir sinai gafa crystals dynamical maps french point ya harmonic 360000 space arise republic hamiltonian chaotic deterministic 2014 proposer manifold 2000 matrices mathematical symbolic despite determinantal physics limit structures vershik decomposition theory dimension government 2015 infinite interval theme translation math hausdorff annals exchange conjecture pfaffian posed arising combinatorics idex transition examples borodin theorems investigation intermediate consolidates kerov olshanski substitution geometric quasi spectral mix 1985 anr dimensional flows computation preprint 02 proof invariant functional solution 2013 investissements geometry last description naturally ergodic surfaces 0001 questions budget katok intense question grassmann origin 11 2012 exhibit chaos

Project "IChaos" 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. telephone: n.a. fax: n.a.
Coordinator Country	France [FR]
Project website	https://www.i2m.univ-amu.fr/Home-ERC-IChaos
Total cost	1˙696˙936 €
EC max contribution	1˙696˙936 € (100%)
Programme	1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
Code Call	ERC-2014-CoG
Funding Scheme	ERC-COG
Starting year	2016
Duration (year-month-day)	from 2016-01-01 to 2020-12-31

Partnership

Take a look of project's partnership.

#	participants	country	role	EC contrib. [€]
1	CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS 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. telephone: n.a. fax: n.a.	FR (PARIS)	coordinator	1˙696˙936.00

Map

Project objective

'The transition from order to chaos has been a central theme of investigation in dynamical systems in the last two decades. Structures that exhibit a mix of deterministic and chaotic properties, for example, quasi-crystals, naturally arise in problems of geometry and mathematical physics. Despite intense study, key questions about these structures remain wide open. The proposed research is an investigation of intermediate chaos in ergodic theory of dynamical systems. Specific examples include systems of geometric origin such as interval exchange maps, translation and Hamiltonian flows on surfaces of higher genus, symbolic substitution systems important in the study of quasi-crystals as well as dynamical systems arising in asymptotic combinatorics and mathematical physics such as determinantal and Pfaffian point processes. Specific tasks include computation of the Hausdorff dimension for the spectral measure of interval exchange maps (problem posed by Ya. Sinai), limit theorems for Hamiltonian flows on surfaces of higher genus (question of A. Katok), development of entropy theory and functional limit theorems for determinantal point processes and a description of the ergodic decomposition for infinite orthogonally-invariant measures on the space of infinite real matrices (the real case of the problem, posed in 2000 by A. Borodin and G. Olshanski, of harmonic analysis on the infinite-dimensional analogue of the Grassmann manifold). The project consolidates the proposer's past work, in particular, his limit theorems for translation flows (Annals of Math. 2014), his proof of the 1985 Vershik-Kerov entropy conjecture (GAFA 2012) and his solution of the complex case of the Borodin-Olshanski problem (preprint 2013). The proposer is currently PI of project ANR-11-IDEX-0001-02 (1.11.2013--30.10.2015; budget 360000 euro) under the Programme 'Investissements d'avenir' of the Government of the French Republic.'

Publications

List of publications.
year	authors and title	journal	last update
2017	Ferenczi, S.; KuÅ‚aga-Przymus, J.; LemaÅ„czyk, M. Sarnak\'s Conjecture -- what\'s new published pages: 65 pages, ISSN: , DOI:	https://arxiv.org/abs/1710.04039 1	2019-05-31
2018	Bufetov, Alexander I.; Solomyak, Boris A spectral cocycle for substitution systems and translation flows published pages: 11 pages, ISSN: , DOI:	arXiv:1802.04783 1	2019-05-31
2018	Alexander I. Bufetov, Yanqi Qiu J-Hermitian determinantal point processes: balanced rigidity and balanced Palm equivalence published pages: 127-188, ISSN: 0025-5831, DOI: 10.1007/s00208-017-1627-y	Mathematische Annalen 371/1-2	2019-05-31
2017	Alexander I. Bufetov, Yanqi Qiu Conditional measures of generalized Ginibre point processes published pages: 4671-4708, ISSN: 0022-1236, DOI: 10.1016/j.jfa.2017.03.004	Journal of Functional Analysis 272/11	2019-05-31
2016	Fan, Shilei; Liao, Lingmin Rational map ax+1/x on the projective line over $mathbb{Q}_2$ published pages: 13 pages, ISSN: , DOI:	https://arxiv.org/abs/1612.01881 1	2019-05-31
2017	Alexander I. Bufetov, Yanqi Qiu Determinantal Point Processes Associated with Hilbert Spaces of Holomorphic Functions published pages: 1-44, ISSN: 0010-3616, DOI: 10.1007/s00220-017-2840-y	Communications in Mathematical Physics 351/1	2019-05-31
2017	Alexander Igorevich Bufetov, Tomoyuki Shirai Quasi-symmetries and rigidity for determinantal point processes associated with de Branges spaces published pages: 1-5, ISSN: 0386-2194, DOI: 10.3792/pjaa.93.1	Proceedings of the Japan Academy, Series A, Mathematical Sciences 93/1	2019-05-31
2016	Bufetov, Alexander I. Conditional measures of determinantal point processes published pages: , ISSN: , DOI:	arXiv:1605.01400 1	2019-05-31
2018	Bufetov, Alexander I.; Dymov, Andrey V.; Osada, Hirofumi The logarithmic derivative for point processes with equivalent Palm measures published pages: 18 pages, ISSN: 0025-5645, DOI:	Journal Mathematical Society of Japan 1	2019-05-31
2017	Alexander I. Bufetov, Yanqi Qiu Ergodic measures on spaces of infinite matrices over non-Archimedean locally compact fields published pages: 2482-2533, ISSN: 0010-437X, DOI: 10.1112/S0010437X17007412	Compositio Mathematica 153/12	2019-05-31
2016	A I Bufetov Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. II. Convergence of infinite determinantal measures published pages: 299-315, ISSN: 1064-5632, DOI: 10.1070/IM8384	Izvestiya: Mathematics 80/2	2019-05-31
2016	Bufetov, Alexander,; Qiu, Yanqi; Shamov, Alexander Kernels of conditional determinantal measures published pages: , ISSN: , DOI:	https://hal.archives-ouvertes.fr/hal-01483603 1	2019-05-31
2017	Bufetov, Alexander I.; Romanov, Roman V. Division subspaces and integrable kernels published pages: 11 pages, ISSN: , DOI:	https://arxiv.org/abs/1707.03463 1	2019-05-31
2017	Bergelson, Vitaly; KuÅ‚aga-Przymus, Joanna; LemaÅ„czyk, Mariusz; Richter, Florian K. A structure theorem for level sets of multiplicative functions and applications published pages: 32 pages, ISSN: , DOI:	https://arxiv.org/abs/1708.02613 1	2019-05-31
2017	Alexander I. Bufetov, Boris Solomyak On ergodic averages for parabolic product flows (Version 3) published pages: 14, ISSN: , DOI:	arXiv:1612.09142	2019-05-31
2017	Alexander I. Bufetov A palm hierarchy for determinantal point processes with the Bessel kernel published pages: 90-97, ISSN: 0081-5438, DOI: 10.1134/s0081543817040058	Proceedings of the Steklov Institute of Mathematics 297/1	2019-05-31
2018	Alexander I. Bufetov, Shilei Fan, Yanqi Qiu Equivalence of Palm measures for determinantal point processes governed by Bergman kernels published pages: , ISSN: 0178-8051, DOI: 10.1007/s00440-017-0803-z	Probability Theory and Related Fields	2019-05-31
2017	Fan, Shilei; Qiu, Yanqi Invariant measures for the actions of the modular group published pages: 5 pages, ISSN: , DOI:	https://arxiv.org/abs/1703.03086 1	2019-05-31
2016	A I Bufetov Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. III. The infinite Bessel process as the limit of the radial parts of finite-dimensional projections of infinite Pickrell measures published pages: 1035-1056, ISSN: 1064-5632, DOI: 10.1070/IM8385	Izvestiya: Mathematics 80/6	2019-05-31
2018	Nizar Demni, Pierre Lazag The Hyperbolic-type Point Process published pages: 12 pages, ISSN: , DOI:	arXiv:1712.04824	2019-05-31
2018	Alexander I Bufetov, Andrey V Dymov A Functional Limit Theorem for the Sine-Process published pages: , ISSN: 1073-7928, DOI: 10.1093/imrn/rny104	International Mathematics Research Notices	2019-05-31
2018	Alexander I. Bufetov, Roman V. Romanov Division subspaces and integrable kernels published pages: 11, ISSN: 0024-6093, DOI: 10.1112/blms.12223	Bulletin of the London Mathematical Society	2019-02-28
2018	Bufetov, Alexander I.; Qiu, Yanqi Patterson-Sullivan measures for point processes and the reconstruction of harmonic functions published pages: 57, ISSN: , DOI:	http://arxiv.org/abs/1806.02306	2019-02-28
2018	Bufetov, Alexander I.; Klimenko, Alexey; Series, Caroline Convergence of spherical averages for actions of Fuchsian Groups published pages: 56, ISSN: , DOI:	http://arxiv.org/abs/1805.11743	2019-02-28

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