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Periodic orbits of discrete and continuous dynamical systems via Poincaré-Miranda theorem
dc.contributor.author | Gasull Embid, Armengol |
dc.contributor.author | Mañosa Fernández, Víctor |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2018-10-22T10:50:55Z |
dc.date.available | 2018-10-22T10:50:55Z |
dc.date.issued | 2018-09-17 |
dc.identifier.citation | Gasull, A., Mañosa, V. "Periodic orbits of discrete and continuous dynamical systems via Poincaré-Miranda theorem". 2018. |
dc.identifier.uri | http://hdl.handle.net/2117/122722 |
dc.description | Preprint |
dc.description.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 Kouchnirenko's conjecture; and an alternative proof of the existence of a class of symmetric central configuration of the $(1+4)$-body problem. |
dc.format.extent | 26 p. |
dc.language.iso | eng |
dc.relation.ispartofseries | arXiv:1809.06208v1 [math.DS] |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics |
dc.subject.lcsh | Differentiable dynamical systems |
dc.subject.other | Periodic orbits |
dc.subject.other | Poincaré-Miranda Theorem |
dc.subject.other | Discrete and continuous dynamical systems |
dc.subject.other | Lotka-Volterra maps |
dc.subject.other | Thue-Morse maps |
dc.subject.other | Discrete Markus-Yamabe conjecture |
dc.subject.other | Kouchnirenko’s conjecture |
dc.subject.other | Limit cycles |
dc.subject.other | Planar piecewise linear systems |
dc.subject.other | Central configurations |
dc.title | Periodic orbits of discrete and continuous dynamical systems via Poincaré-Miranda theorem |
dc.type | External research report |
dc.subject.lemac | Sistemes dinàmics diferenciables |
dc.contributor.group | Universitat Politècnica de Catalunya. CoDAlab - Control, Modelització, Identificació i Aplicacions |
dc.subject.ams | Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory |
dc.subject.ams | Classificació AMS::39 Difference and functional equations::39A Difference equations |
dc.relation.publisherversion | https://arxiv.org/abs/1809.06208 |
dc.rights.access | Open Access |
local.identifier.drac | 23344941 |
dc.description.version | Preprint |
dc.relation.projectid | info:eu-repo/grantAgreement/MINECO/1PE/DPI2016-77407-P |
local.citation.author | Gasull, A.; Mañosa, V. |
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