Characterising blenders via covering relations and cone conditions

We present a characterisation of a blender based on the topological alignment of certain sets in phase space in combination with cone conditions. Importantly, the required conditions can be verified by checking properties of a single iterate of the diffeomorphism, which is achieved by finding finite...

Full description

Saved in:
Bibliographic Details
Published inJournal of Differential Equations Vol. 416; pp. 768 - 805
Main Authors Capiński, Maciej J., Krauskopf, Bernd, Osinga, Hinke M., Zgliczyński, Piotr
Format Journal Article
LanguageEnglish
Published Elsevier Inc 25.01.2025
Subjects
Diffeomorphism
Heterodimensional cycles
Hénon-like map
Invariant manifolds
Partial hyperbolicity
37M21
Diffeomorphism
65G20
37B20
Heterodimensional cycles
37D30
Partial hyperbolicity
Invariant manifolds
Hénon-like map
37C29
Online AccessGet full text

Cover

More Information
Summary:We present a characterisation of a blender based on the topological alignment of certain sets in phase space in combination with cone conditions. Importantly, the required conditions can be verified by checking properties of a single iterate of the diffeomorphism, which is achieved by finding finite series of sets that form suitable sequences of alignments. This characterisation is applicable in arbitrary dimension. Moreover, the approach naturally extends to establishing C1-persistent heterodimensional cycles. Our setup is flexible and allows for a rigorous, computer-assisted validation based on interval arithmetic.
ISSN:0022-0396
DOI:10.1016/j.jde.2024.10.004