Complete Poincar E Sections and Tangent Sets
نویسندگان
چکیده
Trying to extend a local deenition of a surface of section and the corresponding Poincar e map to a global one, one can encounter severe diiculties. We show that global transverse sections often do not exist for Hamiltonian systems with two degrees of freedom. As a consequence we present a method to generate so called W-section, which by construction will be intersected by (almost) all orbits. Depending on the type of the tangent set in the surface of section, we distinguish ve types of W-sections. The method is illustrated by a number of examples, most notably the quartic potential and the double pendulum. W-sections can also be applied to higher-dimensional Hamiltonian systems and to dissipative systems.
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