Abstract.

In this paper, we make an attempt to modify the classic construction of partition of unity (general method of sewing together local smooth objects into a global one) to include the case of objects invariant along a given smooth flow. A class of flows is determined which allow such a construction. A general scheme is presented of obtaining a non-local first integral by sewing together a set of local integrals.

Keywords:

dynamical systems, flows, first integrals.

PP. 104-110.

DOI: 10.14357/20790279180411

References

1. Rabover V.I. Otkrytost’ i zamknutost’ razbienii na orbity gladkogo potoka [Open and closed partitions into orbits of a smooth flow]. Trudy ISA [Proceedings of ISA]. 2014. 64(2): 19 – 26.
2. M. Hirsch. Differential topology. Springer – Verlag. 1976.
3. L. Schwartz. Analyse mathematique. Hermann. 1967.
4. F. Warner. Foundations of Differentiable Manifolds and Lie Groups. Springer – Verlag. 1983.