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Project PN III-P4-ID-PCE-2020-2693 "Dimensions and Invariance in Dynamical Systems" is financed by UEFISCDI - Romania.
Project PN III-P4-ID-PCE-2020-2693 "Dimensions and Invariance in Dynamical Systems" is financed by UEFISCDI - Romania.
Brief Description:
Brief Description:
This research grant is financed by UEFISCDI-Romania and is based at the Institute of Mathematics of the Romanian Academy, Bucharest. The period of the project is January 2021 -- December 2023.
This research grant is financed by UEFISCDI-Romania and is based at the Institute of Mathematics of the Romanian Academy, Bucharest. The period of the project is January 2021 -- December 2023.
Rezumat:
Rezumat:
Acest proiect de cercetare este finantat de UEFISCDI-Romania si se desfasoara la Institutul de Matematica al Academiei Romane, in Bucuresti. Perioada proiectului este Ianuarie 2021 -- Decembrie 2023.
Acest proiect de cercetare este finantat de UEFISCDI-Romania si se desfasoara la Institutul de Matematica al Academiei Romane, in Bucuresti. Perioada proiectului este Ianuarie 2021 -- Decembrie 2023.
Goals of the Project:
Goals of the Project:
In this project we will investigate several research topics in the theory of differentiable dynamical systems, and geometry and analysis on fractals. These topics are related to notions of dimensions of invariant sets and measures for dynamical systems, conformal iterated function systems with or without overlaps, overlap numbers for probability measures on significant classes of fractals, dynamics of holomorphic maps on various complex manifolds, folding entropy, applications in ergodic number theory and in the study of Gibbs states. In this project we will apply notions and methods from thermodynamic formalism and dimension theory, (non)-uniform hyperbolic dynamics for endomorphisms, complex dynamics, differentiable ergodic theory, probability and stochastics on fractals, ergodic number theory. We shall introduce and develop also new ideas, methods and applications in these directions.
In this project we will investigate several research topics in the theory of differentiable dynamical systems, and geometry and analysis on fractals. These topics are related to notions of dimensions of invariant sets and measures for dynamical systems, conformal iterated function systems with or without overlaps, overlap numbers for probability measures on significant classes of fractals, dynamics of holomorphic maps on various complex manifolds, folding entropy, applications in ergodic number theory and in the study of Gibbs states. In this project we will apply notions and methods from thermodynamic formalism and dimension theory, (non)-uniform hyperbolic dynamics for endomorphisms, complex dynamics, differentiable ergodic theory, probability and stochastics on fractals, ergodic number theory. We shall introduce and develop also new ideas, methods and applications in these directions.
Obiectivele Proiectului:
Obiectivele Proiectului:
In acest proiect vom investiga mai multe subiecte de cercetare din teoria sistemelor dinamice diferentiabile, si din geometria si analiza pe fractali. Aceste subiecte sunt legate de notiuni de dimensiune pentru multimi si masuri invariante ale sistemelor dinamice, sisteme iterative de functii cu sau fara suprapuneri, numere de suprapunere pentru masuri probabilistice pe clase importante de fractali, dinamica functiilor olomorfe pe varietati complexe, entropia de infasurare, aplicatii in teoria ergodica a numerelor, si la studiul masurilor Gibbs. In acest proiect vom aplica notiuni si metode de formalism termodinamic si teoria dimensiunii, dinamica uniforma si non-uniforma pentru endomorfisme, dinamica complexa, teorie ergodica diferentiabila, teorie stocastica pe fractali si teoria ergodica a numerelor. Vom introduce si dezvolta deasemenea idei, metode si aplicatii noi in aceste directii.
In acest proiect vom investiga mai multe subiecte de cercetare din teoria sistemelor dinamice diferentiabile, si din geometria si analiza pe fractali. Aceste subiecte sunt legate de notiuni de dimensiune pentru multimi si masuri invariante ale sistemelor dinamice, sisteme iterative de functii cu sau fara suprapuneri, numere de suprapunere pentru masuri probabilistice pe clase importante de fractali, dinamica functiilor olomorfe pe varietati complexe, entropia de infasurare, aplicatii in teoria ergodica a numerelor, si la studiul masurilor Gibbs. In acest proiect vom aplica notiuni si metode de formalism termodinamic si teoria dimensiunii, dinamica uniforma si non-uniforma pentru endomorfisme, dinamica complexa, teorie ergodica diferentiabila, teorie stocastica pe fractali si teoria ergodica a numerelor. Vom introduce si dezvolta deasemenea idei, metode si aplicatii noi in aceste directii.
Team/Echipa:
Team/Echipa:
Eugen Mihailescu (Project Director)
Eugen Mihailescu (Project Director)
Florin Boca
Florin Boca
Radu Munteanu
Radu Munteanu
Raluca Tanase
Raluca Tanase
Remus Radu
Remus Radu
Articles and Preprints/Articole si Preprinturi:
Articles and Preprints/Articole si Preprinturi:
1) E. Mihailescu, Invariant measures in non-conformal fibered systems with singularities, Journal of Functional Analysis, vol 284 (2023), no. 9, paper 109860, 28 pgs, https://doi.org/10.1016/j.jfa.2023.109860.
1) E. Mihailescu, Invariant measures in non-conformal fibered systems with singularities, Journal of Functional Analysis, vol 284 (2023), no. 9, paper 109860, 28 pgs, https://doi.org/10.1016/j.jfa.2023.109860.
2) E. Mihailescu, Thermodynamic formalism for invariant measures in iterated function systems with overlaps, Communications in Contemporary Mathematics, 24 (2022), no. 6, paper 2150041, 27 pgs, World Scientific, DOI: 10.1142/S0219199721500413.
2) E. Mihailescu, Thermodynamic formalism for invariant measures in iterated function systems with overlaps, Communications in Contemporary Mathematics, 24 (2022), no. 6, paper 2150041, 27 pgs, World Scientific, DOI: 10.1142/S0219199721500413.
3) E. Mihailescu and M. Urbanski, Geometry of measures in random systems with complete connections, Journal of Geometric Analysis, vol 32, article 162, 2022, https://doi.org/10.1007/s12220-022-00899-y
3) E. Mihailescu and M. Urbanski, Geometry of measures in random systems with complete connections, Journal of Geometric Analysis, vol 32, article 162, 2022, https://doi.org/10.1007/s12220-022-00899-y
4) A. Bis and E. Mihailescu, Inverse pressure for finitely generated semigroups, Nonlinear Analysis, vol 222, 2022, https://doi.org/10.1016/j.na.2022.112942
4) A. Bis and E. Mihailescu, Inverse pressure for finitely generated semigroups, Nonlinear Analysis, vol 222, 2022, https://doi.org/10.1016/j.na.2022.112942
5) E. Mihailescu, Dimensions of measures, degrees and folding entropy in dynamics, Revue Roumaine de Mathematiques Pures Appl., 68 (2023), no. 1-2, 149-167.
5) E. Mihailescu, Dimensions of measures, degrees and folding entropy in dynamics, Revue Roumaine de Mathematiques Pures Appl., 68 (2023), no. 1-2, 149-167.
6) T. Firsova, R. Radu, R. Tanase, Critical locus for Henon maps in a HOV region; preprint 2022, arXiv:2211.12430.
6) T. Firsova, R. Radu, R. Tanase, Critical locus for Henon maps in a HOV region; preprint 2022, arXiv:2211.12430.
7) E. Mihailescu, R. Munteanu, Inverse measure-theoretic entropy for endomorphisms; preprint 2022.
8) R. Radu, R. Tanase, Global models for the Julia set J^+; preprint 2021.
8) R. Radu, R. Tanase, Global models for the Julia set J^+; preprint 2021.
Dissemination of Results/Diseminarea Rezultatelor:
Dissemination of Results/Diseminarea Rezultatelor:
-- Eugen Mihailescu, Dynamics of semigroups and amalgamated pressure, 10-th Congress of Romanian Mathematicians, Pitesti, July 2023.
-- Dynamical Systems session at the 10-th Congress of Romanian Mathematicians, July 2023, organized by Eugen Mihailescu and Raluca Tanase.
-- Radu Munteanu, Inverse entropy for endomorphisms, 10-th Congress of Romanian Mathematicians, Pitesti, July 2023.
-- Eugen Mihailescu, Dynamics and dimension for a class of skew-product transformations, Conference Dynamics of (Semi)-Group Actions, Poland, June 2023.
-- Eugen Mihailescu, On a class of exact dimensional invariant measures, Conference Fractals and Related Fields IV, Porquerolles, France, September 2022.
-- Radu Munteanu, Inverse measure entropies, Conference Dynamics of (Semi)-Group Actions, Poland, June 2023.
-- Eugen Mihailescu, Thermodynamic formalism for fibered maps with singularities, Univ Lodz, Poland, September 2022.
-- Eugen Mihailescu, Pressures for semigroups of maps, 15-th French-Romanian Analysis Colloquium, Univ Toulouse, France, August 2022.
-- Raluca Tanase, Dynamics of Complex Henon Maps, Connections Workshop: Complex Dynamics, MSRI, Berkeley, USA, February 2022.
-- Remus Radu, Critical points in holomorphic dynamics, Workshop for Young Researchers in Mathematics, 11th edition, IMAR, Romania, May 2022.
-- Raluca Tanase, The Critical Locus of a Dynamical System, Women in Mathematics in South-Eastern Europe, ICMS-Sofia, Bulgaria, December 2022.
-- Eugen Mihailescu, Dynamics for a class of skew-product endomorphisms, Dynamics Seminar (online), Univ. Porto, Portugal, February 2021.
-- Eugen Mihailescu, Pressure functionals in semigroup dynamics, Conference Dynamics of (Semi)-Group Actions, Univ. Lodz, Poland, June 2021.
-- Eugen Mihailescu, Pressure functionals in semigroup dynamics, Conference Dynamics of (Semi)-Group Actions, Univ. Lodz, Poland, June 2021.
-- Remus Radu, Rigidity for complex Henon maps, Dynamics and Computations Seminar, Uppsala Univ, Sweden, May 2021.
-- Remus Radu, Rigidity for complex Henon maps, Dynamics and Computations Seminar, Uppsala Univ, Sweden, May 2021.
-- Raluca Tanase, Holomorphic dynamics in higher dimensions, Workshop for Young Researchers in Mathematics, 10th edition, IMAR, Romania, May 2021.
-- Raluca Tanase, Holomorphic dynamics in higher dimensions, Workshop for Young Researchers in Mathematics, 10th edition, IMAR, Romania, May 2021.
Raport Stiintific 2021:
Raport Stiintific 2021:
Raport-Grant-Dec 2021.pdfRaport Stiintific 2022:
Raport Stiintific 2022:
Raport-Grant-Dec 2022.pdfRaport Stiintific 2023:
Raport Stiintific 2023:
Raport-Grant-Dec 2023.pdfPage updated
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