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Periodic orbits of discrete and continuous dynamical systems via Poincaré-Miranda theorem

Author
Gasull, A.; Mañosa, V.
Type of activity
Report
Date
2018-09-17
Code
arXiv:1809.06208v1 [math.DS]
Project funding
Rate-dependent hysteresis: modeling, analysis and identification, with applications to magnetorheological dampers
Repository
http://hdl.handle.net/2117/122722 Open in new window
URL
https://arxiv.org/abs/1809.06208 Open in new window
Abstract
We present a systematic methodology to determine and locate analytically isolated periodic points of discrete and continuous dynamical systems with algebraic nature. We apply this method to a wide range of examples, including a one-parameter family of counterexamples to the discrete Markus-Yamabe conjecture (La Salle conjecture); the study of the low periods of a Lotka-Volterra-type map; the existence of three limit cycles for a piece-wise linear planar vector field; a new counterexample of Kou...
Citation
Gasull, A., Mañosa, V. "Periodic orbits of discrete and continuous dynamical systems via Poincaré-Miranda theorem". 2018.
Keywords
Central configurations, Discrete Markus-Yamabe conjecture, Discrete and continuous dynamical systems, Kouchnirenko’s conjecture, Limit cycles, Lotka-Volterra maps, Periodic orbits, Planar piecewise linear systems, Poincaré-Miranda Theorem, Thue-Morse maps
Group of research
CoDAlab - Control, Dynamics and Applications

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