Existence of the FS-type renormalisation fixed point for unidirectionally-coupled pairs of maps

Autor:	Andrew Burbanks, Andrew Osbaldestin
Rok vydání:	2023
Předmět:	Statistics and Probability Modeling and Simulation General Physics and Astronomy Statistical and Nonlinear Physics Mathematical Physics
Zdroj:	Journal of Physics A: Mathematical and Theoretical. 56:195202
ISSN:	1751-8121 1751-8113
DOI:	10.1088/1751-8121/acc7dd
Popis:	We give the first proof of the existence of a renormalisation fixed-point for period-doubling in pairs of maps of two variables lying in the so-called Feigenbaum-Summation (FS) universality class. The first map represents a subsystem that is unimodal with an extremum of degree two. The dynamics of the second map accumulates an integral characteristic of the dynamics of the first, via a particular form of unidirectional coupling. We prove the existence of the corresponding renormalisation fixed point by rigorous computer-assisted means and gain tight rigorous bounds on the associated universal constants. Our work provides the first step in establishing rigorously the picture conjectured by Kuznetsov et al of the birth, from the FS-type fixed point, of the so-called C-type two-cycle via a period doubling in the dynamics of the renormalisation group transformation itself.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::2b56e3e8b7bd3a675488aee46269a902 https://doi.org/10.1088/1751-8121/acc7dd Zobrazit plný text záznamu