The Conley Index and Rigorous Numerics for Attracting Periodic Orbits
Despite the enormous number of papers devoted to the problem of the existence of periodic trajectories of differential equations, the theory is still far from satisfactory, especially when concrete differential equations are concerned, because the necessary conditions formulated in many theoretical criteria are difficult to verify in a concrete case. And even if some methods work for some concrete equations, it is usually difficult to carry them over to other problems. Thus quite often the only available method is to experiment numerically. Unfortunately, such an approach cannot be treated as reliable.
KeywordsPeriodic Orbit Periodic Trajectory Index Pair Lorenz Equation Poincare Section
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