Normal forms, resonance and bifurcation analysis via the Carleman linearization

DOI10.1016/0022-247X(89)90233-3zbMath0691.34037OpenAlexW2078691452MaRDI QIDQ582428

Gerasimos Lyberatos, Christos A. Tsiligiannis

Publication date: 1989

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(89)90233-3

zbMATH Keywords

bifurcationresonanceCarleman linear approximationCarleman matrices

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Continua and generalizations (54F15) Nonlinear ordinary differential equations and systems (34A34) Dynamical systems and ergodic theory (37-XX)

Related Items (6)

Computation of the normal form as well as the unfolding of the vector field with zero-zero-Hopf bifurcation at the origin ⋮ BIFURCATION THEORY OF FUNCTIONAL DIFFERENTIAL EQUATIONS: A SURVEY ⋮ An algorithm for computing a new normal form for dynamical systems ⋮ Normal form methods for symbolic creation of approximate solutions of nonlinear dynamical systems ⋮ Analysis of Carleman representation of analytical recursions ⋮ Further reductions of normal forms for dynamical systems

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Steady state bifurcations and exact multiplicity conditions via Carleman linearization
• Non-linear autonomous systems of differential equations and Carleman linearization procedure
• On some questions arising in the approximate solution of nonlinear differential equations
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