Complexity spectrum of some discrete dynamical systems
chao-dyn
2019-08-17 v1 Chaotic Dynamics
Abstract
We first study birational mappings generated by the composition of the matrix inversion and of a permutation of the entries of matrices. We introduce a semi-numerical analysis which enables to compute the Arnold complexities for all the possible birational transformations. These complexities correspond to a spectrum of eighteen algebraic values. We then drastically generalize these results, replacing permutations of the entries by homogeneous polynomial transformations of the entries possibly depending on many parameters. Again it is shown that the associated birational, or even rational, transformations yield algebraic values for their complexities.
Cite
@article{arxiv.chao-dyn/9807031,
title = {Complexity spectrum of some discrete dynamical systems},
author = {N. Abarenkova and J-. Ch. Anglès d'Auriac and S. Boukraa and J. -M. Maillard},
journal= {arXiv preprint arXiv:chao-dyn/9807031},
year = {2019}
}
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