Effective computation of the first Lyapunov quantities for a planar differential equation

A. Gasull; R. Prohens

Applicationes Mathematicae (1997)

  • Volume: 24, Issue: 3, page 243-250
  • ISSN: 1233-7234

Abstract

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We take advantage of the complex structure to compute in a short way and without using any computer algebra system the Lyapunov quantities V 3 and V 5 for a general smooth planar system.

How to cite

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Gasull, A., and Prohens, R.. "Effective computation of the first Lyapunov quantities for a planar differential equation." Applicationes Mathematicae 24.3 (1997): 243-250. <http://eudml.org/doc/219166>.

@article{Gasull1997,
abstract = {We take advantage of the complex structure to compute in a short way and without using any computer algebra system the Lyapunov quantities $V_3$ and $V_5$ for a general smooth planar system.},
author = {Gasull, A., Prohens, R.},
journal = {Applicationes Mathematicae},
keywords = {Lyapunov quantities; weak focus; stability; analytic plane vector field; non-hyperbolic equilibrium; Lyapunov numbers},
language = {eng},
number = {3},
pages = {243-250},
title = {Effective computation of the first Lyapunov quantities for a planar differential equation},
url = {http://eudml.org/doc/219166},
volume = {24},
year = {1997},
}

TY - JOUR
AU - Gasull, A.
AU - Prohens, R.
TI - Effective computation of the first Lyapunov quantities for a planar differential equation
JO - Applicationes Mathematicae
PY - 1997
VL - 24
IS - 3
SP - 243
EP - 250
AB - We take advantage of the complex structure to compute in a short way and without using any computer algebra system the Lyapunov quantities $V_3$ and $V_5$ for a general smooth planar system.
LA - eng
KW - Lyapunov quantities; weak focus; stability; analytic plane vector field; non-hyperbolic equilibrium; Lyapunov numbers
UR - http://eudml.org/doc/219166
ER -

References

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  1. [AL] M. A. M. Alwash and N. G. Lloyd, Non-autonomous equations related to polynomial two-dimensional systems, Proc. Roy. Soc. Edinburgh Sect. A 105 (1987), 129-152. Zbl0618.34026
  2. [ALGM] A. A. Andronov, E. A. Leontovich, I. I. Gordon and A. G. Maier, Theory of Bifurcations of Dynamic Systems on a Plane, Wiley, New York, 1967. 
  3. [CGMM] A. Cima, A. Gasull, V. Ma nosa and F. Ma nosas, Algebraic properties of the Lyapunov and Period constants, Rocky Mountain J. Math., to appear. 
  4. [FLLL] W. W. Farr, C. Li, I. S. Labouriau and W. F. Langford, Degenerate Hopf bifurcation formulas and Hilbert's 16th problem, SIAM J. Math. Anal. 20 (1989), 13-29. Zbl0682.58035
  5. [G] E. Gamero, Computacion simbólica y bifurcaciones de sistemas dinámicos, Ph.D. thesis, Universidad de Sevilla, 1990. 
  6. [GW] F. Göbber and K.-D. Willamowski, Ljapunov approach to multiple Hopf bifurcation, J. Math. Anal. Appl. 71 (1979), 333-350. Zbl0444.34040
  7. [GR] I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products, Academic Press, New York, 1980. Zbl0521.33001
  8. [HW] B. Hassard and Y. H. Wan, Bifurcation formulae derived from center manifold theory, J. Math. Anal. Appl. 63 (1978), 297-312. Zbl0435.34034

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