Critical recurrence in the real quadratic family
(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].
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https://lup.lub.lu.se/record/1c99ca1e-676b-4086-b36d-d7b19824f0d5
- author
- Bylund, Mats LU
- organization
- publishing date
- 2023-10-08
- 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}}, }