Modulus of analytic classification for the generic unfolding of a codimension 1 resonant diffeomorphism or resonant saddle

DOI10.5802/aif.2260zbMath1127.37039OpenAlexW2326140998MaRDI QIDQ2372797

Colin Christopher, Christiane Rousseau

Publication date: 1 August 2007

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2007__57_1_301_0

zbMATH Keywords

modulus of analytic classificationsresonant diffeomorphisms

Mathematics Subject Classification ID

Dynamics induced by flows and semiflows (37C10) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Singularities of holomorphic vector fields and foliations (32S65) Dynamical aspects of holomorphic foliations and vector fields (37F75)

Related Items (11)

The root extraction problem ⋮ Topological rigidity of generic unfoldings of tangent to the identity diffeomorphisms ⋮ Characterization of the generic unfolding of a weak focus ⋮ Unnamed Item ⋮ The modulus of analytic classification for the unfolding of the codimension-one flip and Hopf bifurcations ⋮ The moduli space of germs of generic families of analytic diffeomorphisms unfolding of a codimension one resonant diffeomorphism or resonant saddle ⋮ On the universal unfolding of vector fields in one variable: a proof of Kostov's theorem ⋮ Analytic moduli for unfoldings of germs of generic analytic diffeomorphisms with a codimension parabolic point ⋮ Temporally normalizable generic unfoldings of order-1 weak foci ⋮ Two-parameter unfolding of a parabolic point of a vector field in \(\mathbb{C}\) fixing the origin ⋮ Coalescing Complex Planar Stationary Points

Cites Work

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• Materialization of Poincaré resonances and divergence of normalizing series
• Divergence of series reducing an analytic differential equation to linear normal form at a singular point
• Normalizable, integrable, and linearizable saddle points for complex quadratic systems in \(\mathbb{C}^2\)
• Normalizability, synchronicity, and relative exactness for vector fields in \(\mathbb C^2\)
• Analytical classification of singular saddle-node vector fields
• An analytic classification of saddle resonant singular points of holomorphic vector fields in the complex plane
• Normalizable, integrable and linearizable saddle points in the Lotka-Volterra system
• Classification analytique des équations différentielles non linéaires résonnantes du premier ordre
• Holonomie et intégrales premières
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