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Critical recurrence in the real quadratic family

Bylund, Mats LU (2023) In Ergodic Theory and Dynamical Systems 43(10). p.3255-3287
Abstract

We study recurrence in the real quadratic family and give a sufficient condition on the recurrence rate of the critical orbit such that, for almost every non-regular parameter a, the set of n such that Fn(0;a) is infinite. In particular, when, this extends an earlier result by Avila and Moreira [Statistical properties of unimodal maps: the quadratic family. Ann. of Math. (2) 161(2) (2005), 831-881].

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
critical recurrence, parameter exclusion, real quadratic family
in
Ergodic Theory and Dynamical Systems
volume
43
issue
10
pages
33 pages
publisher
Cambridge University Press
external identifiers
  • scopus:85170842638
ISSN
0143-3857
DOI
10.1017/etds.2022.78
language
English
LU publication?
yes
id
1c99ca1e-676b-4086-b36d-d7b19824f0d5
date added to LUP
2023-12-07 11:02:46
date last changed
2023-12-07 11:03:43
@article{1c99ca1e-676b-4086-b36d-d7b19824f0d5,
  abstract     = {{<p>We study recurrence in the real quadratic family and give a sufficient condition on the recurrence rate of the critical orbit such that, for almost every non-regular parameter a, the set of n such that Fn(0;a) is infinite. In particular, when, this extends an earlier result by Avila and Moreira [Statistical properties of unimodal maps: the quadratic family. Ann. of Math. (2) 161(2) (2005), 831-881].</p>}},
  author       = {{Bylund, Mats}},
  issn         = {{0143-3857}},
  keywords     = {{critical recurrence; parameter exclusion; real quadratic family}},
  language     = {{eng}},
  month        = {{10}},
  number       = {{10}},
  pages        = {{3255--3287}},
  publisher    = {{Cambridge University Press}},
  series       = {{Ergodic Theory and Dynamical Systems}},
  title        = {{Critical recurrence in the real quadratic family}},
  url          = {{http://dx.doi.org/10.1017/etds.2022.78}},
  doi          = {{10.1017/etds.2022.78}},
  volume       = {{43}},
  year         = {{2023}},
}