There are no C^1-stable intersections of regular Cantor sets
Carlos Gustavo Tamm de Araujo Moreira
TL;DR
This paper proves that regular Cantor sets cannot have intersections that remain stable under small C^1 perturbations, highlighting a fundamental limitation in their intersection properties.
Contribution
The paper establishes a new theoretical result demonstrating the non-existence of C^1-stable intersections among regular Cantor sets.
Findings
No C^1-stable intersections exist for regular Cantor sets
Stability of intersections is impossible under C^1 perturbations
Provides insight into the structure and stability properties of Cantor sets
Abstract
We show that there are no C^1-stable intersections of regular Cantor sets.
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Taxonomy
TopicsAdvanced Banach Space Theory · Mathematical Dynamics and Fractals · Holomorphic and Operator Theory