On Transitivities for Skew Products
Nayan Adhikary, Anima Nagar
TL;DR
This paper investigates the transitivity, weakly mixing, and mixing properties of skew product dynamical systems with non-compact fibers, focusing on universality conditions and hypercyclicity criteria.
Contribution
It introduces new conditions and criteria for understanding topological transitivity and hypercyclicity in skew products with non-compact fibers.
Findings
Established universality conditions for skew products
Developed hypercyclicity criteria applicable to these systems
Analyzed the relationships between transitivity, weak mixing, and mixing
Abstract
The dual concepts of `universality' and `hypercyclicity' are better understood and studied as `topological transitivity'. In this article we consider transitivity properties of skew products, essentially with non-compact fibers. We study the `Universality Conditions' and `Hypercyclicity Criterion' associated with the dynamical properties of transitivity, weakly mixing and mixing for these skew products.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory · Holomorphic and Operator Theory