Bifurcation of 2-periodic orbits from non-hyperbolic fixed points
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We introduce the concept of 2-cyclicity for families of one-dimensional maps with a non-hyperbolic fixed point by analogy to the cyclicity for families of planar vector fields with a weak focus. This new concept is useful in order to study the number of 2-periodic orbits that can bifurcate from the fixed point. As an application we study the 2-cyclicity of some natural families of polynomial maps.
CitationCima, A., Gasull, A., Mañosa, V. Bifurcation of 2-periodic orbits from non-hyperbolic fixed points. "Journal of mathematical analysis and applications", Genert 2018, vol. 457, núm. 1, p. 568-584.