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Bifurcation of 2-periodic orbits from non-hyperbolic fixed points |
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| Authors: | Anna Cima Armengol Gasull Víctor Mañosa |
| Affiliation: | 1. Departament de Matemàtiques, Facultat de Ciències, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain;2. Departament de Matemàtiques, Universitat Politècnica de Catalunya, Colom 1, 08222 Terrassa, Spain |
| Abstract: | 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. |
| Keywords: | Non-hyperbolic fixed point Two periodic points Bifurcation Cyclicity |
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