On the first tangency of stable and unstable manifolds in C r planar diffeomorphisms

DOI10.1063/1.529790zbMath0757.58022OpenAlexW1983278455MaRDI QIDQ3991997

Kiyotaka Tanikawa, Yoshihiro Yamaguchi

Publication date: 28 June 1992

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.529790

zbMATH Keywords

stable manifoldsunstable manifoldsfirst asymptotic tangencyfirst direct tangency

Mathematics Subject Classification ID

Stability theory for smooth dynamical systems (37C75)

Related Items

Structure change of stable and unstable manifolds in two-dimensional maps. II: Island-merging and boundary crisis ⋮ Structure change of stable and unstable manifolds in two-dimensional maps: Period-doubling bifurcation ⋮ The first direct heteroclinic tangency theorem in two-dimensional maps ⋮ On the appearance order of homoclinic and heteroclinic intersections in a family of dissipative maps of the plane

Cites Work

• A theorem on the first heteroclinic tangency in two-dimensional maps. Orientation-preserving cases
• A two-dimensional mapping with a strange attractor
• On the creation of homoclinic points
• New type of heteroclinic tangency in two-dimensional maps
• Basin boundary metamorphoses: Changes in accessible boundary orbits
• On Morse-Smale dynamical systems