Abstract
© 2017 Elsevier Inc. 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.
Original language | English |
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Pages (from-to) | 568-584 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 457 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Jan 2018 |
Keywords
- Bifurcation
- Cyclicity
- Non-hyperbolic fixed point
- Two periodic points