Almost Periodic Function

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In mathematics, an almost periodic function is, loosely speaking, a function of a real number that is periodic to within any desired level of accuracy, given suitably long "almost-periods". The concept was first studied by Harald Bohr and later generalized by Vyacheslav Stepanov, Hermann Weyl and Abram Samoilovitch Besicovitch, amongst others. There is also a notion of almost periodic functions on locally compact abelian groups, first studied by John von Neumann. Almost periodicity is a property of dynamical systems that appear to retrace their paths through phase space, but not exactly. An example would be a planetary system, with planets in orbits moving with periods that are not commensurable (i.e., with a period vector that is not proportional to a vector of integers). A theorem of Kronecker from diophantine approximation can be used to show that any particular configuration that occurs once, will recur to within any specified accuracy: if we wait long enough we can observe the planets all return to within a second of arc to the positions they once were in.

Weitere Informationen

  • Allgemeine Informationen
    • GTIN 09786130658076
    • Editor Frederic P. Miller, Agnes F. Vandome, John McBrewster
    • Sprache Englisch
    • Größe H220mm x B150mm x T11mm
    • Jahr 2010
    • EAN 9786130658076
    • Format Fachbuch
    • ISBN 978-613-0-65807-6
    • Titel Almost Periodic Function
    • Untertitel Mathematics, Differentiable manifold, Linear complex structure, Tangent space, Manifold, Complex manifold, Symplectic geometry, Charles Ehresmann, Heinz Hopf, Chern class
    • Gewicht 284g
    • Herausgeber Alphascript Publishing
    • Anzahl Seiten 180
    • Genre Mathematik

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