arXiv 2201.036522022-01-26math.DS

Multiplicity of limit cycles that appear after perturbations of hyperbolic polycycles

Andrei Dukov

备注：: 1 figure, 27 pages, in Russian

英文摘要：

We consider the multiplicity of limit cycles that appear when a hyperbolic polycycle is perturbed. We prove, in particular, that if such unfolding happens in generic finite-parameter families, the multiplicity of every new limit cycle does not exceed the number of separatrix connections in the polycycle.

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