Symplectic topology of integrable dynamical systems. Rough topological classification of classical cases of integrability in the dynamics of a heavy rigid body

1999 ◽  
Vol 94 (4) ◽  
pp. 1512-1557 ◽  
Author(s):  
A. T. Fomenko
Keyword(s):  
Dynamical Systems ◽  
Rigid Body ◽  
Topological Classification ◽  
Symplectic Topology ◽  
Heavy Rigid Body ◽  
Integrable Dynamical Systems

scholarly journals Symmetries and integrability

2008 ◽  
Vol 84 (98) ◽  
pp. 1-36 ◽  
Author(s):  
Bozidar Jovanovic
Keyword(s):  
Dynamical Systems ◽  
Rigid Body ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Hamiltonian Flows ◽  
Finite Dimensional ◽  
Heavy Rigid Body ◽  
Collective Motions ◽  
Invariant Submanifolds ◽  
Integrable Dynamical Systems

This is a survey on finite-dimensional integrable dynamical systems related to Hamiltonian G-actions. Within a framework of noncommutative integrability we study integrability of G-invariant systems, collective motions and reduced integrability. We also consider reductions of the Hamiltonian flows restricted to their invariant submanifolds generalizing classical Hess-Appel'rot case of a heavy rigid body motion.

scholarly journals Discriminantly separable polynomials and the generalized Kowalevski top

2017 ◽  
Vol 44 (2) ◽  
pp. 229-236 ◽  
Author(s):  
Vladimir Dragovic ◽  
Katarina Kukic
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Rigid Body ◽  
Constant Field ◽  
Explicit Integration ◽  
Heavy Rigid Body ◽  
Discriminantly Separable Polynomials ◽  
Integrable Dynamical Systems ◽  
Kowalevski Top

The notion of discriminantly separable polynomials of degree two in each of three variables has been recently introduced and related to a class of integrable dynamical systems. Explicit integration of such systems can be performed in a way similar to Kowalevski?s original integration of the Kowalevski top. Here we present the role of discriminantly separable polynomials in integration of yet another well known integrable system, the so-called generalized Kowalevski top - the motion of a heavy rigid body about a fixed point in a double constant field. We present a novel way to obtain the separation variables for this system, based on the discriminantly separable polynomials.

scholarly journals Dynamics of Bose-Einstein Condensates: Exact Representation and Topological Classification of Coherent Matter Waves

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Leilei Jia ◽  
Qihuai Liu ◽  
Shengqiang Tang
Keyword(s):  
Angular Momentum ◽  
Dynamical Systems ◽  
Bifurcation Theory ◽  
Topological Classification ◽  
Exact Representation ◽  
Matter Waves ◽  
Existence And Multiplicity ◽  
Bose Einstein ◽  
The Waves

By using the bifurcation theory of dynamical systems, we present the exact representation and topological classification of coherent matter waves in Bose-Einstein condensates (BECs), such as solitary waves and modulate amplitude waves (MAWs). The existence and multiplicity of such waves are determined by the parameter regions selected. The results show that the characteristic of coherent matter waves can be determined by the “angular momentum” in attractive BECs while for repulsive BECs; the waves of the coherent form are all MAWs. All exact explicit parametric representations of the above waves are exhibited and numerical simulations support the result.

Baire's Category Theoretic Classification of Compact Expansive Dynamical Systems

2002 ◽  
Vol 09 (04) ◽  
pp. 315-323 ◽  
Author(s):  
Kazutaka Sakai
Keyword(s):  
Dynamical Systems ◽  
Classification Method ◽  
Topological Classification ◽  
Finite Dimensional ◽  
Theoretic Classification

A revised version of the estimation inequality of Akashi [2] is given, and this result is applied to Baire's category theoretic classification of ∊-expansive dynamical systems. Moreover, this classification method is applied to topological classification of shift dynamical systems on finite-dimensional compact domains.

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