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Lebedeva L. V. Phase pictures of standard map of torus. Izvestiya VUZ. Applied Nonlinear Dynamics, 1996, vol. 4, iss. 4, pp. 21-29.

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Language: 
Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
517.9

Phase pictures of standard map of torus

Autors: 
Lebedeva Larisa Vladimirovna, Institute of Applied Mathematics and Cybernetics. Nizhny Novgorod state University
Abstract: 

The standard torus map which defines the dynamics of a number of physical systems is a very complex mathematical object. The ways of transition from regular behaviour to chaos, existence of period doubling bifurcations and bifurcations of heteroclinic structures are the characteristic features of the dynamics of this map rousing the great interest of scientists at present. This paper contains series of phase pictures of standard map of torus with the following: the structure of countability set of different cycles of fixed points, the parametric dependence of structure of phase trajectory set, the velocity of completing of phase torus with separatrix of hyperbolic fixed point.

Key words: 
-
Acknowledgments: 
The work was carried out under the guidance of V.N. Belykh, and the author is very grateful to him for his attentive attitude to this work.
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Received: 
05.06.1995
Accepted: 
17.09.1996
Published: 
10.12.1996
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