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The use of normal forms for analysing nonlinear mechanical vibrations [PDF]
Philosophical Transactions Series A, Mathematical, Physical, and Engineering Sciences, 2015 A historical introduction is given of the theory of normal forms for simplifying nonlinear dynamical systems close to resonances or bifurcation points. The specific focus is on mechanical vibration problems, described by finite degree-of-freedom second ...
Simon A Neild +2 more
exaly +3 more sources
Normal forms for symplectic matrices [PDF]
Portugaliae Mathematica, 2014 We give a self contained and elementary description of normal forms for symplectic matrices, based on geometrical considerations. The normal forms in question are expressed in terms of elementary Jordan matrices and integers with values in \{ -1,0,1\}
J. Gutt
openaire +6 more sources
Birkhoff Normal Forms and KAM Theory for Gumowski-Mira Equation [PDF]
The Scientific World Journal, 2014 By using the KAM theory we investigate the stability of equilibrium solutions of the Gumowski-Mira equation: xn+1=(2axn)/(1+xn2)-xn-1, n=0,1,…, where x-1,x0∈(-∞,∞), and we obtain the Birkhoff normal forms for this equation for different equilibrium ...
M. R. S. Kulenović +2 more
doaj +2 more sources
Normal forms for reduced stochastic climate models. [PDF]
Proc Natl Acad Sci U S A, 2009 Majda AJ, Franzke C, Crommelin D.
europepmc +2 more sources
Van der Pol Equation with a Large Feedback Delay
Mathematics, 2023 The well-known Van der Pol equation with delayed feedback is considered. It is assumed that the delay factor is large enough. In the study of the dynamics, the critical cases in the problem of the stability of the zero equilibrium state are identified ...
Sergey Kashchenko
doaj +1 more source
On the Double-Zero Bifurcation of Jerk Systems
Mathematics, 2023 In this paper, we construct approximate normal forms of the double-zero bifurcation for a two-parameter jerk system exhibiting a non-degenerate fold bifurcation.
Cristian Lăzureanu
doaj +1 more source
Rational Normal Forms and Stability of Small Solutions to Nonlinear Schrödinger Equations [PDF]
Annals of PDE, 2018 We consider general classes of nonlinear Schrödinger equations on the circle with nontrivial cubic part and without external parameters. We construct a new type of normal forms, namely rational normal forms, on open sets surrounding the origin in high ...
J. Bernier, E. Faou, B. Grébert
semanticscholar +1 more source
On the divergence of Birkhoff Normal Forms [PDF]
Publications mathématiques (Bures-sur-Yvette), 2019 It is well known that a real analytic symplectic diffeomorphism of the 2 d $2d$ -dimensional disk ( d ≥ 1 $d\geq 1$ ) admitting the origin as a non-resonant elliptic fixed point can be formally conjugated to its Birkhoff Normal Form, a formal power ...
Raphaël Krikorian
semanticscholar +1 more source
Asymptotics of Regular and Irregular Solutions in Chains of Coupled van der Pol Equations
Mathematics, 2023 Chains of coupled van der Pol equations are considered. The main assumption that motivates the use of special asymptotic methods is that the number of elements in the chain is sufficiently large.
Sergey Kashchenko
doaj +1 more source
Normal Forms for Kummer Surfaces [PDF]
Integrable Systems and Algebraic Geometry, 2018 We determine normal forms for the Kummer surfaces associated with abelian surfaces of polarization of type $(1,1)$, $(1,2)$, $(2,2)$, $(2,4)$, and $(1,4)$.
A. Clingher, Andreas Malmendier
semanticscholar +1 more source