caa a22 4500 475796977 CHVBK 20180406123727.0 cr unu---uuuuu 170329e20001101xx s 000 0 eng 10.1007/PL00001528 doi (NATIONALLICENCE)springer-10.1007/PL00001528 Parabolic fixed points and stability criteria for nonlinear Hill's equation [Elektronische Daten] [D. Núñez, R. Ortega] Abstract.: We discuss the stability of parabolic fixed points of area-preserving mappings and obtain a new proof of a criterion due to Simó. These results are employed to discuss the stability of the equilibrium of certain periodic differential equations of newtonian type. An example is the pendulum of variable length. In this class of equations the First Lyapunov's Method does not apply but in many cases the stability can be characterized in terms of the variational equation. Birkhäuser Verlag, Basel,, 2000 Key words. Stability, parabolic points, pendulum nationallicence Núñez D. Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain, ES aut Ortega R. Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain, ES aut https://doi.org/10.1007/PL00001528 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/PL00001528 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Núñez D. Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain, ES aut NATIONALLICENCE 700 1- Ortega R. Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain, ES aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer