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Normal forms of reversible dynamical systems
International Journal of Theoretical Physics, 1994zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Giuseppe Gaeta, Gaeta Giuseppe
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Two flat normal forms for a class of nonlinear dynamical systems
2010 11th International Conference on Control Automation Robotics & Vision, 2010In this paper we presents two new 0-flat normal forms. It deals with sufficient geometrical conditions which enable us to conclude if a given nonlinear controllable dynamical system can be transformed, by means of change of coordinates, to one of these normal forms. In the same way it gives an algorithm to compute the flat outputs.
Soraya Bououden +2 more
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Normal Forms and Unfoldings for Local Dynamical Systems
Springer Monographs in Mathematics, 2003Preface.- 1. Two Examples.- 2. The splitting problem for linear operators.- 3. Linear Normal Forms.- 4. Nonlinear Normal Forms.- 5. Geometrical Structures in Normal Forms.- 6. Selected Topics in Local Bifurcation Theory.- Appendix A: Rings.- Appendix B: Modules.- Appendix C: Format 2b: Generated Recursive (Hori).- Appendix D: Format 2c: Generated ...
James Murdock
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On the Algebraic Problem Concerning the Normal Forms of Linear Dynamical Systems
American Journal of Mathematics, 1936Introduction. Let m be the number of degrees of freedom of a linear conservative dynamical systenm and let the point (q1, q2,9 * , q'Mn Pl p2, . . . p'mt) of the phase space be denoted by x = (xl, x2, , x.2M). A system of 2m ordinary differential equations of the first order, which are homogeneous, linear and do not contain t explicitly, is a canonical
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The Generalized Normal Forms and Method of Resonance Control of Nonlinear Dynamical Systems
1991 American Control Conference, 1991This paper addresses a new method (named the generalized normal forms (GNF) method) which allows one to find normal forms for the broad class of dynamical systems not considered by earlier techniques. The proposed method is feasible for the dynamical systems with non-smooth and discontinuous non-linearity.
Mark Pinsky
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Lie point-symmetries and Poincare normal forms for dynamical systems
Journal of Physics A: Mathematical and General, 1990The problem of finding the extended Lie-point time-independent symmetries of autonomous systems of ordinary differential equations is compared with the Poincare procedure of reducing the system to linear or normal form, showing a close relationship between the two problems.
CICOGNA, GIAMPAOLO, Gaeta G.
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Normal Forms of Dynamical Systems and Bifurcations
2003We show the existence of a general class of bifurcating solutions to dynamical systems, by introducing their (Poincare-Dulac) normal form, and imposing that the normalizing transformation is convergent. These bifurcating solutions include standard stationary and Hopf bifurcations, and multiple-periodic solutions as well.
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