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Bifurcation of 2-periodic orbits from non-hyperbolic fixed points

Author
Cima, A.; Gasull, A.; Mañosa, V.
Type of activity
Report
Date
2017-07-21
Code
arXiv:1707.06404 [math.DS]
Project funding
Control, dinàmica i aplicacions
Rate-dependent hysteresis: modeling, analysis and identification, with applications to magnetorheological dampers
Repository
http://hdl.handle.net/2117/106815 Open in new window
URL
https://arxiv.org/abs/1707.06404 Open in new window
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.
Citation
Cima, A., Gasull, A., Mañosa, V. "Bifurcation of 2-periodic orbits from non-hyperbolic fixed points". 2017.
Keywords
2-periodic points, Bifurcation, Cyclicity, Non-hyperbolic fixed points
Group of research
CoDAlab - Control, Dynamics and Applications

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