Rigorous computer-assisted bounds on the period doubling renormalisation fixed point and eigenfunctions in maps with critical point of degree 4

Andrew Burbanks*, Andrew Osbaldestin, Judi Thurlby

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Downloads (Pure)

Abstract

We gain tight rigorous bounds on the renormalisation fixed point for period doubling in families of unimodal maps with degree 4 critical point. We use a contraction mapping argument to bound essential eigenfunctions and eigenvalues for the linearisation of the operator and for the operator controlling the scaling of added noise. Multi-precision arithmetic with rigorous directed rounding is used to bound operations in a space of analytic functions yielding tight bounds on power series coefficients and universal constants to over 320 significant figures.
Original languageEnglish
Article number112701
Number of pages18
JournalJournal of Mathematical Physics
Volume62
Issue number11
Early online date3 Nov 2021
DOIs
Publication statusPublished - 30 Nov 2021

Keywords

  • dynamical systems
  • renormalisation group
  • universality
  • period-doubling
  • bifurcations
  • computer-assisted proofs

Fingerprint

Dive into the research topics of 'Rigorous computer-assisted bounds on the period doubling renormalisation fixed point and eigenfunctions in maps with critical point of degree 4'. Together they form a unique fingerprint.

Cite this