KNOTS AND LINKS IN INTEGRABLE HAMILTONIAN SYSTEMS-Reference-Cited by-同舟云学术

KNOTS AND LINKS IN INTEGRABLE HAMILTONIAN SYSTEMS

Published:1998-03 Issue:02 Volume:07 Page:123-153
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

CASASAYAS J.¹,ALFARO J. MARTINEZ²,NUNES A.³

Affiliation:

1. Dept. Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain

2. Dept. Matemàtica Aplicada i Astronomia, Universitat de València, 46100 Burjassot, València, Spain

3. CMAF/Dept. Física Universidade de Lisboa, Campo Grande, C1, 1700 Lisboa, Portugal

Abstract

The main purpose of this paper is to prove that Bott integrable Hamiltonian flows and non-singular Morse-Smale flows are closely related. As a consequence, we obtain a classification of the knots and links formed by periodic orbits of Bott integrable Hamiltonians on the 3-sphere and on the solid torus. We also show that most of Fomenko's theory on the topology of the energy levels of Bott integrable Hamiltonians can be derived from Morgan's results on 3-manifolds that admit non-singular Morse-Smale flows.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216598000097

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