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TOPOLOGICAL AND DYNAMICAL PROPERTIES IN PARAMETERIZED FAMILIES OF NON-HYPERBOLIC ATTRACTORS: THE INVERSE LIMIT APPROACH
National Science Center Poland, Sonata Bis grant 2020-2025
TEAM
SEJAL BABEL
Ph.D. Student
M.Sc. Indian Institute of Technology
B.S. The Maharaja Sayajirao University of Baroda
The project studies parametric families of surface attractors, in parametric families of maps, such as Henon, Lozi, and Arnold families (and others). The focus is on the better understanding of bifurcations (transitions from simple to complex states) of these objects as parameter varies, from the point of view of their geometry (topology) and chaosity of dynamics. This includes continuity of the rotation number of accessible points in the attractors. The study employs the approach of inverse limits, that allow the study of complicated objects, such as fractal-like chaotic attractors, in terms of simpler objects, such as metric trees (dendrites), and their continuous transformations. The dynamical properties of the latter translate into dynamical properties of their natural extensions (shift homeomorphisms), which (semi)conjugate to strongly dissipative planar homeomorphisms. Another tool of interest is symbolic dynamics, which proved to be very useful in the case of multimodal interval maps (Milnor-Thurston kneading theory). However, a transition to dimension two has proved to be challenging so far, and therefore the development of appropriate analogue is of interest.
This project is funded by National Science Center (NCN), Poland in the years 2020-2025, under contract no. 2019/34/E/ST1/00237.
PROJECT PUBLICATIONS, PREPRINTS AND WORK IN PROGRESS
BORONSKI J., STIMAC S; THE PRUNING FRONT CONJECTURE, FOLDING PATTERNS AND CLASSIFICATION OF HENON MAPS IN THE PRESENCE OF STRANGE ATTRACTORS, arXiv:2302.12568v2
BOROŃSKI J.; LINKED ORBITS OF HOMEOMORPHISMS OF THE PLANE AND GAMBAUDO-KOLEV THEOREM, MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY (2024), TO APPEAR
BORONSKI J., STIMAC S; DENSELY BRANCHING TREES AS MODELS FOR HENON-LIKE AND LOZI-LIKE ATTRACTORS, ADV. MATH. 429 (2023), 109191, 27 pp.
BORONSKI J., CINC J., OPROCHA P.; BEYOND 0 AND ∞: A SOLUTION TO THE BARGE ENTROPY CONJECTURE, SUBMITTED
BORONSKI J., MINC, P., STIMAC S; ON CONJUGACY OF NATURAL EXTENSIONS OF 1-DIMENSIONAL MAPS, ERGODIC THEORY AND DYNAMICAL SYSTEMS, DOI:10.1017/ETDS.2022.62
OU D-S, CRITICAL POINTS IN HIGHER DIMENSIONS, I: REVERSE ORDER OF PERIODIC ORBIT CREATIONS IN THE LOZI FAMILY, SUBMITTED
FORYŚ-KRAWIEC M., HANTAKOVA J., KUPKA J.,OPROCHA P., ROTH S., DENDRITES AND MEASURES WITH DISCRETE SPECTRUM, ERGODIC THEORY AND DYNAMICAL SYSTEMS DOI:10.1017/ETDS.2021.157
FORYŚ-KRAWIEC M., HANTAKOVA J., OPROCHA P.,ON THE STRUCTURE OF ALPHA-LIMIT SETS, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS DOI:10.3934/DCDS.2021159
KUCHARSKI P., ON CARTWRIGHT-LITTLEWOOD FIXED POINT THEOREM, INDAGATIONES MATHEMATICAE DOI:10.1016/J.INDAG.2022.02.009
KUCHARSKI P., GRAPH COVERS OF HIGHER DIMENSIONAL DYNAMICAL SYSTEMS, TOPOLOGY APPL. 315 (2022), PAPER NO. 108145, 8 PP.
KUCHARSKI P., STRANGE ATTRACTORS FOR THE FAMILY OF ORIENTATION PRESERVING LOZI MAPS, CHAOS 33, 113121 (2023); doi: 10.1063/5.0139893
BOROŃSKI J., OU D-S, DISCONTINUITIES IN PRIME END ROTATION NUMBERS OF HENON ATTRACTORS, IN PREPARATION
BORONSKI J., CLARK A., KUCHERENKO T., ROTATION SETS OF PARAMETRIC FAMILIES OF ATTRACTORS ON THE TORUS, IN PROGRESS
BOROŃSKI J., OU D-S, DISCONTINUITIES IN PRIME END ROTATION NUMBERS OF LOZI ATTRACTORS, IN PREPARATION
BORONSKI J., KUCHARSKI P., OU D-S, LOZI MAPS WITH PERIODIC POINTS OF ALL PERIODS N > 13, PREPRINT
BORONSKI J., MARTENS M., PALMISANO L., STIMAC S., ON INFINITELY RENEORMALIZABLE HENON MAPS, IN PROGRESS
BORONSKI J., FORYS-KRAWIEC M., KUCHARSKI P., STIMAC S. A RENORMALIZATION MODEL FOR ORIENTATION REVERSING LOZI MAPS, IN PREPARATION
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