On the Arnold’s Classification Conjecture on Dynamics Of Complexity of Linear Intersections

Let X , Y be two linear subspaces of the m -dimensional complex space ℂ m with m > 1. The dimensions of the subspaces X and Y are k and m − k respectively and let F : ℂ m → ℂ m be a non-degenerate linear operator. In this work, we study the properties of the intersection between the subspace Y an...

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Bibliographic Details
Published inJournal of dynamical and control systems Vol. 29; no. 3; pp. 1019 - 1035
Main Author de Nova-Vázquez, Mónica
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2023
Springer Nature B.V
Subjects
Calculus of Variations and Optimal Control; Optimization
Classification
Complexity
Control
Dynamical Systems
Dynamical Systems and Ergodic Theory
Intersections
Linear operators
Mathematics
Mathematics and Statistics
Subspaces
Systems Theory
Vibration
37E30
Complementary dimensions
iteration
Dynamic of intersection
37C25
Linear subspaces
No transversality
37E15
37F05
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Summary:Let X , Y be two linear subspaces of the m -dimensional complex space ℂ m with m > 1. The dimensions of the subspaces X and Y are k and m − k respectively and let F : ℂ m → ℂ m be a non-degenerate linear operator. In this work, we study the properties of the intersection between the subspace Y and the n -iteration of the subspace X under F . In the case when the dimension of the subspace X is either one or two, we give some results about a geometrical classification when we obtain an infinite set of moments n of no transversality between the space Y and the n -iteration of X under F .
ISSN:1079-2724
1573-8698
DOI:10.1007/s10883-022-09637-7