Piecewise rotations: limit set for the non -bijective maps
Nicolas B\'edaride, Jean fran\c{c}ois Bertazzon, Idrissa, Kabor\'e
TL;DR
This paper investigates non-bijective piecewise rotations of the plane, providing new upper bounds on their limit set size, thus advancing understanding of their dynamical behavior.
Contribution
It introduces improved upper bounds for the limit set size of non-bijective piecewise rotations, refining previous results in the field.
Findings
Derived new upper bounds for the limit set size
Enhanced understanding of the dynamics of non-bijective piecewise rotations
Improved upon previous theoretical results
Abstract
We consider non-bijective piecewise rotations of the plane. These maps belong to a family introduced in previous papers by Boshernitzan and Goetz. We derive in this paper some upper bounds to the size of the limit set. This improves results of \cite{Bosh.Goet.03}.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric and Algebraic Topology · Advanced Differential Equations and Dynamical Systems