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Large amplitude oscillations for a class of symmetric polynomial differential systems in R³ Anais da ABC (AABC)
Llibre,Jaume; Messias,Marcelo.
In this paper we study a class of symmetric polynomial differential systems in R³, which has a set of parallel invariant straight lines, forming degenerate heteroclinic cycles, which have their two singular endpoints at infinity. The global study near infinity is performed using the Poincaré compactification. We prove that for all n <FONT FACE=Symbol>Î</FONT> N there is epsilonn > 0 such that for 0 < epsilon < epsilonn the system has at least n large amplitude periodic orbits bifurcating from the heteroclinic loop formed by the two invariant straight lines closest to the x-axis, one contained in the half-space y > 0 and the other in y < 0.
Tipo: Info:eu-repo/semantics/article Palavras-chave: Infinite heteroclinic loops; Periodic orbits; Symmetric systems.
Ano: 2007 URL: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652007000400001
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Lines of principal curvature on canal surfaces in R³ Anais da ABC (AABC)
Garcia,Ronaldo; Llibre,Jaume; Sotomayor,Jorge.
In this paper are determined the principal curvatures and principal curvature lines on canal surfaces which are the envelopes of families of spheres with variable radius and centers moving along a closed regular curve in R³. By means of a connection of the differential equations for these curvature lines and real Riccati equations, it is established that canal surfaces have at most two isolated periodic principal lines. Examples of canal surfaces with two simple and one double periodic principal lines are given.
Tipo: Info:eu-repo/semantics/article Palavras-chave: Riccati equation; Principal curvature lines; Canal surfaces.
Ano: 2006 URL: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652006000300002
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