Diffeomorphisms on surfaces with a finite number of moduli

DOI10.1017/S0143385700004120zbMath0609.58023OpenAlexW1969455151MaRDI QIDQ3749797

Welington De Melo, Sebastian J. van Strien

Publication date: 1987

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385700004120

zbMATH Keywords

invariant foliationsaxiom A diffeomorphismsappearance of modulidiffeomorphisms on two dimensional manifoldsdifferentiable version of the lambda lemmastructural stability theorem

Mathematics Subject Classification ID

Ordinary differential equations and systems on manifolds (34C40) Stability theory for smooth dynamical systems (37C75) Morse-Smale systems (37D15)

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Classification of the simplest diffeomorphisms of the sphere \(S^{2}\) with one stability modulus ⋮ Moduli of stability for germs of homogeneous vectorfields on \(R^ 3\) ⋮ Moduli of 3-dimensional diffeomorphisms with saddle-foci ⋮ Realization of cascades on surfaces with finitely many moduli of topological conjugacy ⋮ Mathematical problems of nonlinear dynamics: A tutorial ⋮ A type of moduli for saddle connections of planar diffeomorphisms ⋮ Stability of vector fields on \({\mathbb{R}}^ 3\) determined by the first non- vanishing jet ⋮ Infinitely many moduli of stability at the dissipative boundary of chaos ⋮ Moduli of surface diffeomorphisms with cubic tangencies ⋮ Necessary and sufficient conditions for the topological conjugacy of surface diffeomorphisms with a finite number of orbits of heteroclinic tangency ⋮ Necessary and sufficient conditions for the topological conjugacy of 3-diffeomorphisms with heteroclinic tangencies ⋮ Quasi-transversal saddle-node bifurcation on surfaces ⋮ On models with non-rough Poincaré homoclinic curves ⋮ Smooth linearization of hyperbolic fixed points without resonance conditions ⋮ Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms

Cites Work

• Moduli of stability of two-dimensional diffeomorphisms
• Structural stability of diffeomorphisms on two-manifolds
• On Morse-Smale dynamical systems
• A structural stability theorem
• Differentiable dynamical systems

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