Realization of the Numerical Invariant of the Seifert Fibration of Integrable Systems by Billiards
V. V. Vedyushkina, В. А. Кибкало
Abstract
A local version of the Fomenko conjecture on the possibility of the realization of the Liouville foliation with the Fomenko–Zieschang arbitrary topological invariant, which is a graph with numerical labels, by integrable billiards is discussed. It is proved that Liouville foliation with an arbitrary value of the integer mark which defines the Euler class of the Seifert manifold is algorithmically realized in the class of billiard books.
Topics & Concepts
MathematicsFibrationFoliation (geology)Integrable systemInvariant (physics)ConjectureDynamical billiardsPure mathematicsEuler's formulaRealization (probability)Mathematical analysisMathematical physicsGeometryHomotopyGeologyMetamorphic rockStatisticsGeochemistryQuantum chaos and dynamical systemsMathematical Dynamics and FractalsAdvanced Differential Equations and Dynamical Systems