Smooth linearization of hyperbolic fixed points without resonance conditions

DOI10.1016/0022-0396(90)90089-8zbMath0726.58039OpenAlexW2055476104MaRDI QIDQ804049

Sebastian J. van Strien

Publication date: 1990

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(90)90089-8

zbMATH Keywords

Hartman-Grobman theoremhyperbolic fixed point\(C^ 2\)-diffeomorphisms

Mathematics Subject Classification ID

Normal forms for dynamical systems (37G05) Dynamical systems with hyperbolic behavior (37D99)

Related Items (20)

Partial linearization for noninvertible mappings ⋮ \(C^1\)-continuation of periodic orbits from homoclinics ⋮ Minimal measures on the level sets below Mañé critical value ⋮ Distributional convergence in planar dynamics and singular perturbations ⋮ Smooth dependence of nonautonomous linearization on parameters ⋮ On local linearization of control systems ⋮ Lagrangian descriptors for two dimensional, area preserving, autonomous and nonautonomous maps ⋮ Smooth linearization of nonautonomous coupled systems ⋮ Differentiability of the conjugacy in the Hartman-Grobman Theorem ⋮ Sharpness for \(C^1\) linearization of planar hyperbolic diffeomorphisms ⋮ Multidimensional discrete dynamical systems with slow behavior ⋮ On the nonexistence of iterative roots ⋮ -Hölder linearization of hyperbolic diffeomorphisms with resonance ⋮ New method of smooth extension of local maps on linear topological spaces. Applications and examples ⋮ \(a\)-Hölder linearization ⋮ Conjugacy of normally tangent diffeomorphisms: A tool for treating moduli of stability ⋮ \(\sigma\)-Hölder continuous linearization near hyperbolic fixed points in \(\mathbb{R}^n\) ⋮ On Hölder dependence of the parameterized Hartman-Grobman theorem ⋮ A note on differentiability of the conjugacy in a delayed version of Hartman-Grobman theorem ⋮ On classification of the Poincaré type maps on \(\mathbb{R}^3\)

Cites Work

• Normal hyperbolicity and linearisability
• On the Structure of Local Homeomorphisms of Euclidean n-Space, II
• Smooth Linearization Near a Fixed Point
• Diffeomorphisms on surfaces with a finite number of moduli
• Singularities of vector fields on ℝ³ determined by their first non-vanishing jet
• On a Theorem of P. Hartman
• On the Local Linearization of Differential Equations
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