| dc.creator | Artés, Joan C. | |
| dc.creator | Llibre, Jaume | |
| dc.creator | Teixeira, Marco Antonio | |
| dc.date | 2011-01-01 | |
| dc.date | 2014-12-23T13:15:29Z | |
| dc.date | 2015-11-26T11:41:38Z | |
| dc.date | 2014-12-23T13:15:29Z | |
| dc.date | 2015-11-26T11:41:38Z | |
| dc.date.accessioned | 2018-03-28T20:45:17Z | |
| dc.date.available | 2018-03-28T20:45:17Z | |
| dc.identifier | Computational & Applied Mathematics. Sociedade Brasileira de Matemática Aplicada e Computacional, v. 30, n. 2, p. 463-483, 2011. | |
| dc.identifier | 1807-0302 | |
| dc.identifier | S1807-03022011000200012 | |
| dc.identifier | 10.1590/S1807-03022011000200012 | |
| dc.identifier | http://dx.doi.org/10.1590/S1807-03022011000200012 | |
| dc.identifier | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000200012 | |
| dc.identifier | http://www.repositorio.unicamp.br/jspui/handle/REPOSIP/44552 | |
| dc.identifier | http://www.repositorio.unicamp.br/handle/REPOSIP/44552 | |
| dc.identifier | http://repositorio.unicamp.br/jspui/handle/REPOSIP/44552 | |
| dc.identifier.uri | http://repositorioslatinoamericanos.uchile.cl/handle/2250/1234846 | |
| dc.description | We consider one-parameter families of 2-dimensional vector fields Xµ having in a convenient region R a semistable limit cycle of multiplicity 2m when µ = 0, no limit cycles if µ < 0, and two limit cycles one stable and the other unstable if µ > 0. We show, analytically for some particular families and numerically for others, that associated to the semistable limit cycle and for positive integers n sufficiently large there is a power law in the parameter µ of the form µn ≈ Cnα< 0 with C, α ∈ R, such that the orbit of Xµn through a point of p ∈ R reaches the position of the semistable limit cycle of X0 after given n turns. The exponent α of this power law depends only on the multiplicity of the semistable limit cycle, and is independent of the initial point p ∈ R and of the family Xµ. In fact α = -2m/(2m - 1). Moreover the constant C is independent of the initial point p ∈ R, but it depends on the family Xµ and on the multiplicity 2m of the limit cycle Γ. | |
| dc.description | 463 | |
| dc.description | 483 | |
| dc.language | en | |
| dc.publisher | Sociedade Brasileira de Matemática Aplicada e Computacional | |
| dc.relation | Computational & Applied Mathematics | |
| dc.rights | aberto | |
| dc.source | SciELO | |
| dc.subject | semistable limit cycle | |
| dc.subject | semistable fixed point | |
| dc.subject | universal constant | |
| dc.subject | power law | |
| dc.title | A universal constant for semistable limit cycles | |
| dc.type | Artículos de revistas | |
