Bifurcations of Relative Equilibria
نویسندگان
چکیده
منابع مشابه
Drift bifurcations of relative equilibria and transitions of spiral waves
We consider dynamical systems that are equivariant under a noncompact Lie group of symmetries and the drift of relative equilibria in such systems In particular we investigate how the drift for a parametrized family of normally hyperbolic relative equilibria can change character at what we call a drift bifurcation To do this we use results of Arnold to analyze parametrized families of elements ...
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Resonant and nonresonantHopf bifurcations from relative equilibria posed in two spatial dimensions, in systems with Euclidean SE(2) symmetry, have been extensively studied in the context of spiral waves in a plane and are now well understood. We investigate Hopf bifurcations from relative equilibria posed in systems with compact SO(3) symmetry where SO(3) is the group of rotations in three dime...
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Relative equilibria and relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems and occur for example in celestial mechanics, molecular dynamics and rigid body motion. Relative equilibria are equilibria and RPOs are periodic orbits of the symmetry reduced system. Relative Lyapunov centre bifurcations are bifurcations of relative periodic orbits from relative equilibria c...
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For Hamiltonian systems with spherical symmetry there is a marked difference between zero and non-zero momentum values, and amongst all relative equilibria with zero momentum there is a marked difference between those of zero and those of non-zero angular velocity. We use techniques from singularity theory to study the family of relative equilibria that arise as a symmetric Hamiltonian which ha...
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ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 1990
ISSN: 0036-1410,1095-7154
DOI: 10.1137/0521081