Normal forms, holomorphic linearization and generic bifurcations of dynamic equations on discrete time scales

DOI10.1007/s10884-022-10177-8WikidataQ115382823 ScholiaQ115382823MaRDI QIDQ6196037

Milan Medved'

Publication date: 14 March 2024

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

zbMATH Keywords

saddle-node bifurcationexponential stabilitylinearizationtime scalesnormal formsgeneric bifurcation

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Stability of solutions to ordinary differential equations (34D20) Dynamic equations on time scales or measure chains (34N05)

Cites Work

• Nonautonomous bifurcation of bounded solutions. II: A shovel-bifurcation pattern
• Analysis on measure chains - a unified approach to continuous and discrete calculus
• Topological decoupling, linearization and perturbation on inhomogeneous time scales
• A simple global characterization for normal forms of singular vector fields
• Global characterization of the normal form for a vector field near a closed orbit
• Normal forms for nonautonomous differential equations
• A spectral characterization of exponential stability for linear time-invariant systems on time scales
• Normal forms for nonautonomous difference equations
• Generic one-parameter families of vector fields on two-dimensional manifolds
• Singularities of vector fields
• Nonautonomous bifurcation of bounded solutions. I: a Lyapunov-Schmidt approach
• Stability results for higher dimensional equations on time scales
• Generic properties of parametrized vectorfields. I
• Generic properties of parametrized vectorfields. II
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item