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arXiv · 1804.06587

A route to chaos in the Boros-Moll map

Laura Gardini·Víctor Mañosa·Iryna Sushko
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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.

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Laura Gardini, Víctor Mañosa, Iryna Sushko. 2018-04-18. A route to chaos in the Boros-Moll map. https://doi.org/10.1142/s021812741930009x

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