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Conley Conjecture
The Conley conjecture, named after mathematician Charles Conley, is a mathematical conjecture in the field of symplectic geometry, a branch of differential geometry. Background Let (M, \omega) be a compact symplectic manifold. A vector field V on M is called a Hamiltonian vector field if the 1-form \omega( V, \cdot) is exact (i.e., equals to the differential of a function H. A Hamiltonian diffeomorphism \phi: M \to M is the integration of a 1-parameter family of Hamiltonian vector fields V_t, t \in , 1/math>. In dynamical systems In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a p ... one would like to understand the distribution of fixed points or periodic points. A periodic point of a Hamiltonian diffeomorphism \phi (of periodic k) is a point x \in M such that \phi^k(x) = x . A fe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles C
Charles is a masculine given name predominantly found in English language, English and French language, French speaking countries. It is from the French form ''Charles'' of the Proto-Germanic, Proto-Germanic name (in runic alphabet) or ''*karilaz'' (in Latin alphabet), whose meaning was "free man". The Old English descendant of this word was ''Churl, Ċearl'' or ''Ċeorl'', as the name of King Cearl of Mercia, that disappeared after the Norman conquest of England. The name was notably borne by Charlemagne (Charles the Great), and was at the time Latinisation of names, Latinized as ''Karolus'' (as in ''Vita Karoli Magni''), later also as ''Carolus (other), Carolus''. Some Germanic languages, for example Dutch language, Dutch and German language, German, have retained the word in two separate senses. In the particular case of Dutch, ''Karel'' refers to the given name, whereas the noun ''kerel'' means "a bloke, fellow, man". Etymology The name's etymology is a Common ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |