光滑仿射二次曲面 3 折叠的一些有趣的分层变形 *

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-05-20 DOI:10.1088/1361-6544/ad48f3

Cinzia Bisi, Jonathan D Hauenstein and Tuyen Trung Truong

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引用次数: 0

摘要

我们研究了在复数上的光滑仿射二次曲面 3 折叠的双动力映射族，其形式为常数，似乎具有一些（以及许多其他）有趣/意料之外的特征：（a）它们是同调双曲的；（b）它们的第二动力度是代数数而不是代数整数；以及（c）它们的周期点的对数增长严格小于它们的代数熵。这些映射是保留每个四元数的多项式映射的限制。本文的研究是严格研究与实验研究的结合，其中实验研究我们依赖于 Bertini，它是一个可靠而快速的软件，可用于复杂代数几何中昂贵的数值计算。

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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Some interesting birational morphisms of smooth affine quadric 3-folds *

We study a family of birational maps of smooth affine quadric 3-folds, over the complex numbers, of the form constant, which seems to have some (among many others) interesting/unexpected characters: (a) they are cohomologically hyperbolic, (b) their second dynamical degree is an algebraic number but not an algebraic integer, and (c) the logarithmic growth of their periodic points is strictly smaller than their algebraic entropy. These maps are restrictions of a polynomial map on preserving each of the quadrics. The study in this paper is a mixture of rigorous and experimental ones, where for the experimental study we rely on Bertini which is a reliable and fast software for expensive numerical calculations in complex algebraic geometry.

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来源期刊

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.