Sergey V. Gonchenko, Lev M. Lerman, Andrey L. Shilnikov, Dmitry V. Turaev
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引用次数: 0
摘要
本文回顾了L. P. Shilnikov关于同斜混沌的研究成果，重点介绍了他对周期轨道和不变环面的庞卡罗同斜混沌的重要贡献。此外，我们讨论了他在非自治和无限维系统中的相关发现。这篇综述延续了我们之前的回顾[1]，我们研究了Shilnikov在同斜轨道分岔上的突破性成果——他将A. A. Andronov和E. A. Leontovich的经典工作从平面扩展到多维自治系统，以及他在鞍焦点环和螺旋混沌方面的开创性发现。
Scientific Heritage of L. P. Shilnikov. Part II. Homoclinic Chaos
We review the works initiated and developed by L. P. Shilnikov on homoclinic chaos, highlighting his fundamental contributions to Poincaré homoclinics to periodic orbits and invariant tori. Additionally, we discuss his related findings in non-autonomous and infinite-dimensional systems. This survey continues our earlier review [1], where we examined Shilnikov’s groundbreaking results on bifurcations of homoclinic orbits — his extension of the classical work by A. A. Andronov and E. A. Leontovich from planar to multidimensional autonomous systems, as well as his pioneering discoveries on saddle-focus loops and spiral chaos.
期刊介绍：
Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.
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