Convergence of normal form transformations: The role of symmetries

Acta Applicandae Mathematicae

Volumn 70, Issue 1-3, 2002, Pages 95-111

  Cicogna, Giampaolo ^a,c   Walcher, Sebastian ^b,c  

^a UNIVERSITY OF PISA   (Italy)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^c INSTITUTE OF EPIDEMIOLOGY   (Germany)

Author keywords

Bifurcations; Convergence of normalizing transformations; Dynamical systems; Lie point symmetries; Poincar Dulac normal forms

Indexed keywords

BIFURCATION (MATHEMATICS); DIFFERENTIAL EQUATIONS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; VECTORS;

NORMALIZING TRANSFORMATIONS;

NONLINEAR SYSTEMS;

EID: 0036124439     PISSN: 01678019     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1013922131043     Document Type: Article

References (28)

1. Ordinary differential equations
2. Mathematical aspects of classical and celestial mechanics
3. Normal forms, symmetry and linearization of dynamical systems
4. Local theory of nonlinear analytic ordinary differential equations
5. Analytical form of differential equations
6. Symmetries and convergence of normalizing transformations
7. On the convergence of normalizing transformations in the presence of symmetries
8. Convergent normal forms of symmetric dynamical systems
9. Resonant bifurcations
10. Poincaré normal forms and Lie point symmetries
11. Symmetry and perturbation theory in nonlinear dynamics
12. Nonlinear symmetries and normal forms
13. A simple global characterization for normal forms of singular vector fields
14. On the reduction of an analytic system of differential equations to the normal form by an analytic transformation
15. Classification analytique des équations differentielles non lineaires résonnantes du premier ordre
16. On the reduction of an analytic system of differential equations to linear form
17. The Hamiltonian Hopf bifurcation
18. On differential equations in normal form
19. On convergent normal form transformations in presence of symmetries
20. On the Poincaré problem
21. Plane polynomial vector fields with prescribed invariant curves