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Topologically mildly mixing of higher orders along generalized polynomials.
- Source :
-
Journal of Differential Equations . Oct2024, Vol. 406, p174-201. 28p. - Publication Year :
- 2024
-
Abstract
- This paper is devoted to studying the multiple recurrent property of topologically mildly mixing systems along generalized polynomials. We show that if a minimal system is topologically mildly mixing, then it is mild mixing of higher orders along generalized polynomials. Precisely, suppose that (X , T) is a topologically mildly mixing minimal system, d ∈ N , p 1 , ... , p d are integer-valued generalized polynomials with (p 1 , ... , p d) non-degenerate. Then for all non-empty open subsets U , V 1 , ... , V d of X , { n ∈ Z : U ∩ T − p 1 (n) V 1 ∩ ... ∩ T − p d (n) V d ≠ ∅ } is an IP⁎-set. [ABSTRACT FROM AUTHOR]
- Subjects :
- *POLYNOMIALS
Subjects
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 406
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 178421470
- Full Text :
- https://doi.org/10.1016/j.jde.2024.06.009