کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4613899 1339274 2016 24 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Global bifurcations close to symmetry
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Global bifurcations close to symmetry
چکیده انگلیسی

Heteroclinic cycles involving two saddle-foci, where the saddle-foci share both invariant manifolds, occur persistently in some symmetric differential equations on the 3-dimensional sphere. We analyse the dynamics around this type of cycle in the case when trajectories near the two equilibria turn in the same direction around a 1-dimensional connection — the saddle-foci have the same chirality. When part of the symmetry is broken, the 2-dimensional invariant manifolds intersect transversely creating a heteroclinic network of Bykov cycles. We show that the proximity of symmetry creates heteroclinic tangencies that coexist with hyperbolic dynamics. There are n-pulse heteroclinic tangencies — trajectories that follow the original cycle n times around before they arrive at the other node. Each n  -pulse heteroclinic tangency is accumulated by a sequence of (n+1)(n+1)-pulse ones. This coexists with the suspension of horseshoes defined on an infinite set of disjoint strips, where the first return map is hyperbolic. We also show how, as the system approaches full symmetry, the suspended horseshoes are destroyed, creating regions with infinitely many attracting periodic solutions.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 444, Issue 1, 1 December 2016, Pages 648–671
نویسندگان
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