广义Manin变换和QRT映射

IF 1 Q3 Engineering

Journal of Computational Dynamics Pub Date : 2018-06-14 DOI:10.3934/JCD.2021009

Peter H. van der Kamp, D. McLaren, G. Quispel

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引用次数: 10

摘要

许多变换是平面的映射，它保留了一束三次曲线。我们将其推广到保存二次、某些四次和更高次铅笔的映射，并表明它们是保存度量的。完整的18参数QRT映射是在两个双基点趋于无穷极限的四次情形下的一个特例。另一方面，每个广义Manin变换都可以通过分数仿射变换转化为qrt形式。我们也对承认有根的广义Manin变换进行了分类。

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Generalised Manin transformations and QRT maps

Manin transformations are maps of the plane that preserve a pencil of cubic curves. We generalise to maps that preserve quadratic, and certain quartic and higher degree pencils, and show they are measure preserving. The full 18-parameter QRT map is obtained as a special instance of the quartic case in a limit where two double base points go to infinity. On the other hand, each generalised Manin transformation can be brought into QRT-form by a fractional affine transformation. We also classify the generalised Manin transformations which admit a root.

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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.