Symmetries and Topology of Dynamical Systems with two Degrees of Freedom

  • Valery Kozlov
Part of the NATO ASI Series book series (NSSB, volume 331)


Let M be a closed two-dimensional surface viewed as a configuration space of a dynamical system with two degrees of freedom. We denote the local coordinates on M by q 1, q 2. In mechanics they are usually called the generalized coordinates. Let p 1, p 2 be canonical momenta conjugated with q 1, q 2. Hence,
$$ x = \left( {{q_1},{q_2},{p_1},{p_2}} \right) $$
are local coordinates in the phase space T*M (the cotangent bundle of the surface M).


Cotangent Bundle Geodesic Flow Positive Definite Quadratic Form Quadratic Integral Symmetry Field 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Valery Kozlov
    • 1
  1. 1.Department of Mathematics and MechanicsMoscow State UniversityMoscowRussia

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