The criticality of centers of potential systems at the outer boundary

F. Mañosas; D. Rojas; J. Villadelprat

doi:https://doi.org/10.1016/j.jde.2015.11.040

The criticality of centers of potential systems at the outer boundary

F. Mañosas, D. Rojas, J. Villadelprat

Department of Mathematics

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

10 Citations (Scopus)

Abstract

© 2015 Elsevier Inc. The number of critical periodic orbits that bifurcate from the outer boundary of a potential center is studied. We call this number the criticality at the outer boundary. Our main results provide sufficient conditions in order to ensure that this number is exactly 0 and 1. We apply them to study the bifurcation diagram of the period function of X=-y∂x+((x+1)p-(x+1)q)∂y with q<p. This family was previously studied for q=1 by Y. Miyamoto and K. Yagasaki.

Original language	English
Pages (from-to)	4918-4972
Journal	Journal of Differential Equations
Volume	260
Issue number	6
DOIs	https://doi.org/10.1016/j.jde.2015.11.040
Publication status	Published - 15 Mar 2016

Keywords

Bifurcation
Center
Critical periodic orbit
Criticality
Period function

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title = "The criticality of centers of potential systems at the outer boundary",

abstract = "{\textcopyright} 2015 Elsevier Inc. The number of critical periodic orbits that bifurcate from the outer boundary of a potential center is studied. We call this number the criticality at the outer boundary. Our main results provide sufficient conditions in order to ensure that this number is exactly 0 and 1. We apply them to study the bifurcation diagram of the period function of X=-y∂x+((x+1)p-(x+1)q)∂y with q<p. This family was previously studied for q=1 by Y. Miyamoto and K. Yagasaki.",

keywords = "Bifurcation, Center, Critical periodic orbit, Criticality, Period function",

author = "F. Ma{\~n}osas and D. Rojas and J. Villadelprat",

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TY - JOUR

T1 - The criticality of centers of potential systems at the outer boundary

AU - Mañosas, F.

AU - Rojas, D.

AU - Villadelprat, J.

PY - 2016/3/15

Y1 - 2016/3/15

N2 - © 2015 Elsevier Inc. The number of critical periodic orbits that bifurcate from the outer boundary of a potential center is studied. We call this number the criticality at the outer boundary. Our main results provide sufficient conditions in order to ensure that this number is exactly 0 and 1. We apply them to study the bifurcation diagram of the period function of X=-y∂x+((x+1)p-(x+1)q)∂y with q<p. This family was previously studied for q=1 by Y. Miyamoto and K. Yagasaki.

AB - © 2015 Elsevier Inc. The number of critical periodic orbits that bifurcate from the outer boundary of a potential center is studied. We call this number the criticality at the outer boundary. Our main results provide sufficient conditions in order to ensure that this number is exactly 0 and 1. We apply them to study the bifurcation diagram of the period function of X=-y∂x+((x+1)p-(x+1)q)∂y with q<p. This family was previously studied for q=1 by Y. Miyamoto and K. Yagasaki.

KW - Bifurcation

KW - Center

KW - Critical periodic orbit

KW - Criticality

KW - Period function

U2 - https://doi.org/10.1016/j.jde.2015.11.040

DO - https://doi.org/10.1016/j.jde.2015.11.040

M3 - Article

SN - 0022-0396

VL - 260

SP - 4918

EP - 4972

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 6

ER -

The criticality of centers of potential systems at the outer boundary

Abstract

Keywords

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