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RESEARCH PRODUCT
Bifurcations of Links of Periodic Orbits in Mathieu Systems
J. Martínez AlfaroB. Campossubject
PhysicsPhysics and Astronomy (miscellaneous)media_common.quotation_subjectInfinitysymbols.namesakeClassical mechanicsMathieu functionHopf linkPhase spaceOrbit (dynamics)symbolsPeriodic orbitsAstrophysics::Earth and Planetary AstrophysicsBifurcationmedia_commondescription
We prove that orbits escape from infinity, and that therefore the sphere S can be considered as its phase space. If the parameter δ is large enough, the system is non-singular MorseSmale, and its periodic orbits define a Hopf link. As δ decreases, the system undergoes some bifurcations that we describe geometrically. We relate the bifurcation orbits to periodic orbits continued from the linear Mathieu equation.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2000-07-01 | Progress of Theoretical Physics |