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N. Magnitskii, S. Sidorov (2007)
Application of the Feigenbaum-Sharkovskii-Magnitskii theory to the analysis of Hamiltonian systemsDifferential Equations, 43
E. Goldfain (2008)
Bifurcations and Pattern Formation in Particle Physics: An Introductory StudyEur. Phys. Lett., 82
Ervin Goldfain (2007)
Bifurcations and pattern formation in particle physics: An introductory studyEPL (Europhysics Letters), 82
N. Magnitskii (2008)
The New Approach to Analysis of Hamiltonian Systems
N.A. Magnitskii (2008)
New Approach to the Analysis of Hamiltonian and Conservative SystemsDiffer. Uravn., 44
N.A. Magnitskii (2007)
Universal Theory of Dynamic and Space-Time Chaos in Complex SystemsDin. Slozh. Sist., 1
J. Carlson, A. Jaffe, A. Wiles (2006)
The Millennium Prize Problems
N. Magnitskii (2008)
New approach to the analysis of Hamiltonian and conservative systemsDifferential Equations, 44
N.A. Magnitskii (2009)
On the Nature of Dynamic Chaos in a Neighborhood of a Separatrix of a Conservative SystemDiffer. Uravn., 45
N. Magnitskii (2009)
On the nature of dynamic chaos in a neighborhood of a separatrix of a conservative systemDifferential Equations, 45
S.G. Matinyan (1985)
Dynamic Chaos of Nonabelian Gauge FieldsFiz. Elem. Chast. Atomn. Yadra, 16
N.A. Magnitskii, S.V. Sidorov (2007)
Application of the Feigenbaum-Sharkovskii-Magnitskii Theory to the Analysis of Hamiltonian SystemsDiffer. Uravn., 43
In the present paper, we consider a scenario of transition to chaotic dynamics in the Hamiltonian system of homogeneous Yang-Mills fields with two degrees of freedom in the case of the Higgs mechanism. We show that in such a system, as well as in other Hamiltonian and conservative systems of equations, the nonlocal effect of multiplication of hyperbolic and elliptic cycles and tori around elliptic cycles in neighborhoods of the separatrix surfaces of hyperbolic cycles plays a key role on the initial stage of transition from a regular motion to a chaotic one. We observe that the new elliptic and hyperbolic cycles of the Hamiltonian system are generated as stable and saddle cycles of the extended dissipative system of equations not only as a result of saddle-node bifurcations but also as a result of fork-type bifurcations.
Differential Equations – Springer Journals
Published: Jan 21, 2010
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