1993/05/17 by Carmen Chicone, Chicone, Carmen
Mathematics · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.chao-dyn/9305007
openalex publication_date 1993/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally nondegenerate. The bifurcation function whose zeros are the bifurcation points for families of perturbed periodic solutions is determined. This result is applied to find the periodic solutions near resonance for a two degree of freedom mechanical system modeling a rotor interacting with an elastic support.