Article

On the geometry of Hamiltonian vector fields

Abdigappar NarmanovNational University of Uzbekistan, 100174, 4 University, Tashkent, UzbekistanBekzod DiyarovNational University of Uzbekistan, 100174, 4 University, Tashkent, Uzbekistan

E3S Web of Conferencesjournal2023en

ABI

Abstract

It is known that vector fields play an important role in many areas of mathematics and technology, in particular, in the theory of dynamical systems. Hamiltonian dynamical systems are generated by Hamiltonian vector fields. The paper studies the geometry of a singular foliation of a four-dimensional Euclidean space generated by the orbits of two Hamiltonian vector fields. It is proved that the regular leaf of this foliation is a surface of positive normal curvature and nonzero normal torsion.

Topics

Nonlinear Waves and Solitons Advanced Differential Equations and Dynamical Systems Quantum chaos and dynamical systems

Identifiers

DOI: 10.1051/e3sconf/202345809013

Citations and references

Cited by 06 references

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