Slow-fast torus knots

DOI10.36045/j.bbms.220208zbMath1525.34086arXiv2103.05989MaRDI QIDQ6073805

Renato Huzak, Hildeberto Jardón-Kojakhmetov

Publication date: 18 September 2023

Published in: Bulletin of the Belgian Mathematical Society - Simon Stevin (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.05989

zbMATH Keywords

limit cyclestorus knotsslow-fast systemsslow divergence integral

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Ordinary differential equations and systems on manifolds (34C40) Singular perturbations for ordinary differential equations (34E15) Canard solutions to ordinary differential equations (34E17) Low-dimensional topology in specific dimensions (57K99)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ducks on the torus: existence and uniqueness
• Cyclicity of common slow-fast cycles
• Knots and links in three-dimensional flows
• Generic torus canards
• The Poincaré-Bendixson theorem: from Poincaré to the XXIst century
• Duck farming on the two-torus: multiple canard cycles in generic slow-fast systems
• Duck factory on the two-torus: multiple canard cycles without geometric constraints
• Canard cycles in generic fast-slow systems on the torus
• A Generalization of Hermite's Interpolation Formula
• Canard cycles and center manifolds
• A Generalization of a Poincare-Bendixson Theorem to Closed Two-Dimensional Manifolds