A route to chaos in the Boros-Moll map
Abstract
The Boros-Moll map appears as a subsystem of a Landen transformation associated to certain rational integrals and its dynamics is related to the convergence of them. In the paper, we study the dynamics of a one-parameter family of maps which unfolds the Boros-Moll one, showing that the existence of an unbounded invariant chaotic region in the Boros-Moll map is a peculiar feature within the family. We relate this singularity with a specific property of the critical lines that occurs only for this special case. In particular, we explain how the unbounded chaotic region in the Boros-Moll map appears. Special attention is devoted to explain the main contact/homoclinic bifurcations that occur in the family. We also report some other bifurcation phenomena that appear in the considered unfolding.
Keywords
Cite
@article{arxiv.1804.06587,
title = {A route to chaos in the Boros-Moll map},
author = {Laura Gardini and Víctor Mañosa and Iryna Sushko},
journal= {arXiv preprint arXiv:1804.06587},
year = {2019}
}
Comments
20 pages, 22 figures