Limit Cycles of Differential Equations pp 55-61 | Cite as

# The Tangential Center-Focus Problem

Chapter

## Abstract

As is well known, the second part of Hilbert’s 16th problem is concerned with bounding the number of limit cycles in a polynomial system (1.2) of degree where the Hamiltonian,

*n*in terms of*n*. This is a very hard problem, but Arnold has suggested a “Weak Hilbert’s 16th problem” which seems far more tractable: to find a bound on the number of limit cycles which can bifurcate from a first-order perturbation of a Hamiltonian system,$$
\dot x = - \frac{{\partial H}}
{{\partial y}} + \varepsilon P,\dot y = \frac{{\partial H}}
{{\partial x}} + \varepsilon Q,
$$

(7.1)

*H*, is a polynomial of degree*n*+ 1 and the perturbation terms,*P*and*Q*are polynomials of degree*m*.## Keywords

Riemann Surface Homology Group Polynomial System Perturbation Term Dehn Twist
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Birkhäuser Verlag 2007