Re-factorising a QRT map

IF 1 Q3 Engineering

Journal of Computational Dynamics Pub Date : 2019-06-02 DOI:10.3934/jcd.2019016

N. Joshi, P. Kassotakis

引用次数: 4

Abstract

A QRT map is the composition of two involutions on a biquadratic curve: one switching the $x$-coordinates of two intersection points with a given horizontal line, and the other switching the $y$-coordinates of two intersections with a vertical line. Given a QRT map, a natural question is to ask whether it allows a decomposition into further involutions. Here we provide new answers to this question and show how they lead to a new class of maps, as well as known HKY maps and quadrirational Yang-Baxter maps.

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重构QRT映射

QRT映射是双二次曲线上的两个对合图的组合:一个用给定的水平线交换两个交点的x坐标，另一个用垂直线交换两个交点的y坐标。给定一个QRT映射，一个自然的问题是问它是否允许分解成进一步的卷积。在这里，我们为这个问题提供了新的答案，并展示了它们如何导致一类新的地图，以及已知的HKY地图和四次方杨-巴克斯特地图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational Dynamics Engineering-Computational Mechanics

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： JCD is focused on the intersection of computation with deterministic and stochastic dynamics. The mission of the journal is to publish papers that explore new computational methods for analyzing dynamic problems or use novel dynamical methods to improve computation. The subject matter of JCD includes both fundamental mathematical contributions and applications to problems from science and engineering. A non-exhaustive list of topics includes * Computation of phase-space structures and bifurcations * Multi-time-scale methods * Structure-preserving integration * Nonlinear and stochastic model reduction * Set-valued numerical techniques * Network and distributed dynamics JCD includes both original research and survey papers that give a detailed and illuminating treatment of an important area of current interest. The editorial board of JCD consists of world-leading researchers from mathematics, engineering, and science, all of whom are experts in both computational methods and the theory of dynamical systems.