Invariant Parallels, Invariant Meridians and Limit Cycles of Polynomial Vector Fields on Some 2-Dimensional Algebraic Tori in ℝ3

Jaume Llibre; Salomón Rebollo-Perdomo

doi:https://doi.org/10.1007/s10884-013-9315-4

Invariant Parallels, Invariant Meridians and Limit Cycles of Polynomial Vector Fields on Some 2-Dimensional Algebraic Tori in ℝ³

Jaume Llibre, Salomón Rebollo-Perdomo

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

5 Citations (Scopus)

Abstract

We consider the polynomial vector fields of arbitrary degree in ℝ3 having the 2-dimensional algebraic torus, where l, m and n positive integers, and r ∈ (1, ∞), invariant by their flow. We study the possible configurations of invariant meridians and parallels that these vector fields can exhibit on T2(l, m, n). Furthermore, we analyze when these invariant meridians or parallels are limit cycles. © 2013 Springer Science+Business Media New York.

Original language	English
Pages (from-to)	777-793
Journal	Journal of Dynamics and Differential Equations
Volume	25
Issue number	3
DOIs	https://doi.org/10.1007/s10884-013-9315-4
Publication status	Published - 1 Sept 2013

Keywords

2-Dimensional torus
Invariant meridian
Invariant parallel
Limit cycle
Periodic orbit
Polynomial vector field

Access to Document

https://doi.org/10.1007/s10884-013-9315-4

https://ddd.uab.cat/record/150652

Cite this

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title = "Invariant Parallels, Invariant Meridians and Limit Cycles of Polynomial Vector Fields on Some 2-Dimensional Algebraic Tori in ℝ3",

abstract = "We consider the polynomial vector fields of arbitrary degree in ℝ3 having the 2-dimensional algebraic torus, where l, m and n positive integers, and r ∈ (1, ∞), invariant by their flow. We study the possible configurations of invariant meridians and parallels that these vector fields can exhibit on T2(l, m, n). Furthermore, we analyze when these invariant meridians or parallels are limit cycles. {\textcopyright} 2013 Springer Science+Business Media New York.",

keywords = "2-Dimensional torus, Invariant meridian, Invariant parallel, Limit cycle, Periodic orbit, Polynomial vector field",

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T1 - Invariant Parallels, Invariant Meridians and Limit Cycles of Polynomial Vector Fields on Some 2-Dimensional Algebraic Tori in ℝ3

AU - Llibre, Jaume

AU - Rebollo-Perdomo, Salomón

PY - 2013/9/1

Y1 - 2013/9/1

N2 - We consider the polynomial vector fields of arbitrary degree in ℝ3 having the 2-dimensional algebraic torus, where l, m and n positive integers, and r ∈ (1, ∞), invariant by their flow. We study the possible configurations of invariant meridians and parallels that these vector fields can exhibit on T2(l, m, n). Furthermore, we analyze when these invariant meridians or parallels are limit cycles. © 2013 Springer Science+Business Media New York.

AB - We consider the polynomial vector fields of arbitrary degree in ℝ3 having the 2-dimensional algebraic torus, where l, m and n positive integers, and r ∈ (1, ∞), invariant by their flow. We study the possible configurations of invariant meridians and parallels that these vector fields can exhibit on T2(l, m, n). Furthermore, we analyze when these invariant meridians or parallels are limit cycles. © 2013 Springer Science+Business Media New York.

KW - 2-Dimensional torus

KW - Invariant meridian

KW - Invariant parallel

KW - Limit cycle

KW - Periodic orbit

KW - Polynomial vector field

U2 - https://doi.org/10.1007/s10884-013-9315-4

DO - https://doi.org/10.1007/s10884-013-9315-4

M3 - Article

SN - 1040-7294

VL - 25

SP - 777

EP - 793

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

IS - 3