Title: Hidden Regularity of Stability Boundaries in Two-step Hill’s Equations
Abstract: Stability boundaries in a three-parameter space for Hill’s equation with two-step periodic potentials are studied. Their geometric structure is described completely in the elliptic–elliptic case, by analyzing the monodromy matrix of the system in a three-parameter setting, namely the two frequencies involved and their time ratio in each period. In particular, we show that there exist some families of curves where the monodromy matrix is plus or minus the identity, organizing the whole bifurcation set. After introducing new suitable parameters, expressions for stability boundaries become much simpler: The structure of resonance pockets shows periodicity with respect to two of the three parameters and its hidden regularity is unveiled.
Publication Year: 2021
Publication Date: 2021-07-19
Language: en
Type: book-chapter
Indexed In: ['crossref']
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