Mathematical　SurveysMonographsシリーズの最新刊発売中！

AMSのMathematical　SurveysMonographsシリーズの最新刊、発売中です！

Degree Theory and Symmetric Equations Assisted by GAP　System
(Mathematical Surveys and Monographs Vol. 286)

●著者：Balanov, Zalman/Krawcewicz, Wieslaw/Rachinskii, Dmitrii/Wu, Hao?pin/Yu, Jianshe
●出版社：American Mathematical Society
●ISBN： 978-1-4704-7713-4
●刊行：2025/02
●paper/660P

純粋および応用数学解析の研究者、大学院生、対称現象の数学的モデリングに関わる分野に関心のある科学者など、解析学と代数学の基礎知識を持つ読者を対象としています。

Symmetries are a common feature of real-world phenomena in many fields, including physics, biology, materials science, and engineering. They can help understand the behavior of a system and optimize engineering designs. Nonlinear effects such as delays, nonsmoothness, and hysteresis can have a significant impact on the dynamics and contribute to the increased complexity of symmetric systems. The goal of this book is to provide a complete theoretical and practical manual for studying a large class of dynamical problems with symmetries using degree theory methods. To study the impact of symmetries on the occurrence of periodic solutions in dynamical systems, special variants of the Brouwer degree, the Brouwer equivariant degree, and the twisted equivariant degree are developed to predict patterns, regularities, and symmetries of solutions. Applications to specific dynamical systems and examples are supported by a software package integrated with the GAP system, which provides assistance in the group-theoretic computations involved in equivariant analysis. This book is intended for readers with a basic knowledge of analysis and algebra, including researchers in pure and applied mathematical analysis, graduate students, and scientists interested in areas involving mathematical modeling of symmetric phenomena. The text is self-contained, and the necessary background material is provided in the appendices.

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