Existence of horseshoe sets with nondegenerate one-sided homoclinic tangencies in \(\mathbb R^3\)

DOI10.14492/HOKMJ/1253539582zbMath1147.37017OpenAlexW2026406004MaRDI QIDQ933225

Yusuke Nishizawa

Publication date: 21 July 2008

Published in: Hokkaido Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.14492/hokmj/1253539582

zbMATH Keywords

homoclinic tangencieshyperbolic fixed pointsBirkhoff-Smale Theoremhorseshoe setssingular \(\lambda\)-lemma

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Dynamical systems with hyperbolic orbits and sets (37D05) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

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