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<p>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 [<CitationRef CitationID="CR1">1</CitationRef>], 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.</p>

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Scientific Heritage of L. P. Shilnikov. Part II. Homoclinic Chaos

  • 期刊论文

  • 发表日期：

    2025年4月7日

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  • Sergey V. Gonchenko,
  • Lev M. Lerman,
  • Andrey L. Shilnikov,
  • Dmitry V. Turaev

摘要

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.