Exact circular Morse functions, Morse-type inequalities and integrals of Hamiltonian systems
type: Item
instance of: scholarly article
title: Exact circular Morse functions, Morse-type inequalities and integrals of Hamiltonian systems
zbMATH Open document ID: 0699.58024
DOI: 10.1007/BF01060557
author: A. T. Fomenko
author: V. Sharko
published in: Ukrainian Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: The circular Morse functions (for which the critical points form non- degenerate critical circles) are investigated. It is pointed out, that such functions appear frequently as integrals of motion of classical Hamiltonian systems. The apparatus of a combinatorial character (graphs associated with circular Morse functions) is worked out. In this way the authors represent substantial aspects of the situation when the decomposition to round handles take place. The inequalities of the Morse type are proved for the Morse functions on an arbitrary smooth manifold (of the dimension \(\geq 2):\) it is shown that the lower bounds of the number of critical circles with index \(\lambda\) of a given circular Morse function are determined by the homology groups of the manifold in question. A new proof of the existence of an exact circular Morse function is presented.
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 37D15
Mathematics Subject Classification ID: 57R70
zbMATH DE Number: 4147138
zbMATH Keywords: Morse inequalities
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: critical circles
zbMATH Keywords: Morse function
reviewed by: P. Prešnajder
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01060557
OpenAlex ID: W2026839639
description: scientific article; zbMATH DE number 4147138