caa a22 4500 477036996 CHVBK 20180405111307.0 cr unu---uuuuu 170330e19961101xx s 000 0 eng 10.1007/BF02434054 doi (NATIONALLICENCE)springer-10.1007/BF02434054 A generalization of the theory of normal forms [Elektronische Daten] [W. Warner, P. Sethna, J. Sethna] Summary: Normal forms allow the use of a restricted class of coordinate transformations (typically homogeneous polynomials) to put the bifurcations found in nonlinear dynamical systems into a few standard forms. We investigate here the consequences of relaxing the restrictions of the form of the coordinate transformations. In the Duffing equation, a logarithmic transformation can remove the nonlinearity: in one interpretation, the nonlinearity is replaced by a branch cut leading to a Poincaré section. When the linearized problem is autonomous with diagonal Jordan form, we can remove all nonlinearities order by order using these singular coordinate transformations. Springer-Verlag New York Inc, 1996 normal forms nationallicence bifurcations nationallicence Duffing equation nationallicence Poincaré section nationallicence Lie transform nationallicence nonlinear Stokes phenomena nationallicence Warner W. Aerospace Engineering and Mechanics, University of Minnesota, 107 Akerman Hall, 110 Union St. S.E., 55455, Minneapolis, MN, USA aut Sethna P. Aerospace Engineering and Mechanics, University of Minnesota, 107 Akerman Hall, 110 Union St. S.E., 55455, Minneapolis, MN, USA aut Sethna J. Department of Physics, Cornell University, 14853, Ithaca, NY, USA aut Journal of Nonlinear Science Springer-Verlag 6/6(1996-11-01), 499-506 0938-8974 6:6<499 1996 6 332 https://doi.org/10.1007/BF02434054 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02434054 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Warner W. Aerospace Engineering and Mechanics, University of Minnesota, 107 Akerman Hall, 110 Union St. S.E., 55455, Minneapolis, MN, USA aut NATIONALLICENCE 700 1- Sethna P. Aerospace Engineering and Mechanics, University of Minnesota, 107 Akerman Hall, 110 Union St. S.E., 55455, Minneapolis, MN, USA aut NATIONALLICENCE 700 1- Sethna J. Department of Physics, Cornell University, 14853, Ithaca, NY, USA aut NATIONALLICENCE 773 0- Journal of Nonlinear Science Springer-Verlag 6/6(1996-11-01), 499-506 0938-8974 6:6<499 1996 6 332 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer