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Meromorphic Non-Integrability of Several 3D Dynamical Systems

Kaiyin Huang, Shaoyun Shi, Wenlei Li
2017 Entropy  
In this paper, we apply the differential Galoisian approach to investigate the meromorphic non-integrability of a class of 3D equations in mathematical physics, including Nosé-Hoover equations, the Lü  ...  Our main results show that all these considered systems are, in fact, non-integrable in nearly all parameters.  ...  Non-Integrability In what follows, we will apply the systematic Galoisian approach concluded in the previous section to investigate the meromorphic non-integrability of several 3D systems, including Noseé-Hoover  ... 
doi:10.3390/e19050211 fatcat:wyihe77kvrahranpee6ketlqui

Page 6091 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
The authors intend, as mentioned in the title and introduction, to prove the meromorphic non-integrability of the motion of a particle around a massive straight segment.  ...  Introduction: “All dynamic systems exhibit some degree of inter- nal damping.  ... 

On Exact Solution of a Classical 3D Integrable Model

S.M. Sergeev
2000 Journal of Nonlinear Mathematical Physics  
Dynamical variables for the evolution model are the coefficients of these systems of linear equations.  ...  For one, this determinant is the generating functions of all integrals of motion for the evolution, and on the other hand it defines a high genus algebraic curve.  ...  Spatial nature of any 3d integrable model means that geometrically linear variables are assigned to several elements of 3d cubic lattice. This assignment gives a type of the linear system.  ... 
doi:10.2991/jnmp.2000.7.1.5 fatcat:jyptlvq62vbq7prjdgke2a5y5m

On the meromorphic non-integrability of some $N$-body problems

Juan Morales-Ruiz, Sergi Simon
2009 Discrete and Continuous Dynamical Systems. Series A  
We present a proof of the meromorphic nonintegrability of the planar N -Body Problem for some special cases.  ...  The N -Body Problem with equal masses is also proven non-integrable.  ...  The nal draft of this paper was written during a short stay in the UMPA ENS-Lyon; we acknowledge Alexei Tsygvintsev for his invitation.  ... 
doi:10.3934/dcds.2009.24.1225 fatcat:7lrmzdhdpjh4hiuvgjrmshhm6y

Meromorphy and topology of localized solutions in the Thomas–MHD model

J.-D. FOURNIER, S. GALTIER
2001 Journal of Plasma Physics  
The one-dimensional MHD system first introduced by J.H. Thomas [Phys. Fluids 11, 1245 (1968 ] as a model of the dynamo effect is thoroughly studied in the limit of large magnetic Prandtl number.  ...  Theoretically, the proof of the partial integrability backs up the role ascribed to meromorphy. Practically, predictions are derived for MHD plasmas.  ...  Festou for correspondence on solar system plasmas. Some remarks by A.C. Newell stimulated us to pursue the study of the partially integrable character of the system, and E.  ... 
doi:10.1017/s002237780100887x fatcat:4v2vwwujn5hddga76ozhkg5ebe

Dualities in integrable systems andN= 2 SUSY theories

A Gorsky
2001 Journal of Physics A: Mathematical and General  
We discuss dualities of the integrable dynamics behind the exact solution to the N=2 SUSY YM theory.  ...  We argue that there are analogues of S duality as well as 3d mirror symmetry in the many-body systems of Hitchin type governing low-energy effective actions.  ...  The action variables in dynamical system are the integrals of meromorphic differential λ over the A-cycles on the spectral curve.  ... 
doi:10.1088/0305-4470/34/11/329 fatcat:yj54eduwcjdn3pw4nzdkh6fl4a

Page 665 of Mathematical Reviews Vol. , Issue 2002A [page]

2002 Mathematical Reviews  
, for saddle-node bifurcations P(t) ~ 1-3 up tor ~hi a 2002a:82052 82B40 35D05 35D10 35805 Alexandre, Radjesvarane (F-ORLN-AM; Orléans) Around 3D Boltzmann non linear operator without angular cutoff, a  ...  Summary: “We consider the statistical distribution of zeros of ran- dom meromorphic functions whose poles are independent random variables.  ... 

Spectral curves and parameterizations of a discrete integrable 3-dimensional model [article]

S. Pakuliak, S. Sergeev
2002 arXiv   pre-print
We consider a discrete classical integrable model on the 3-dimensional cubic lattice.  ...  The solutions of this model can be used to parameterize the Boltzmann weights of the different 3-dimensional spin models.  ...  ) or classical integrable systems associated with several 3-dimensional lattices.  ... 
arXiv:nlin/0209019v1 fatcat:jd5mtc2ds5asdjhpsrdtraejdy

Using the Taylor Center to Teach ODEs

Alexander Gofen
2012 CODEE Journal  
The Taylor Center also offers dynamic graphics (including 3D stereo vision).  ...  After a brief review of the features of the Taylor Center, we consider instructive examples of ODEs in various applications and also several particular examples illustrating intricacies of numeric integration  ...  dynamic graphics (including 3D stereo vision with conventional monitors and anaglyph Red/Blue glasses).  ... 
doi:10.5642/codee.201209.01.06 fatcat:bscm2ciqkvhmvp57vfxbrj7rwy

On a q-Central Limit Theorem Consistent with Nonextensive Statistical Mechanics

Sabir Umarov, Constantino Tsallis, Stanly Steinberg
2008 Milan Journal of Mathematics  
Wendroff), Development and Analysis of 3D Non-Split Optimally Stable Lax-Wendroff Type Difference Scheme for Conservation Laws, in Symbolic and Numerical Scientific Computation organized by Franz Winkler  ...  MEETINGS ATTENDED (without presenting) March 05 Keystone Symposium: Systems Biology: Integrating Biology, Technology and Computation.  ... 
doi:10.1007/s00032-008-0087-y fatcat:3gyzvzh2ang3xihs2t5tfzkujm

On multiply-connected Fatou components in iteration of meromorphic functions

Jian-Hua Zheng
2006 Journal of Mathematical Analysis and Applications  
Therefore, we give out several criterion conditions for non-existence of the Baker wandering domains.  2005 Elsevier Inc. All rights reserved.  ...  Let f : C →Ĉ be a transcendental meromorphic function with at most finitely many poles.  ...  some relationship between theory of complex dynamics and value distribution of meromorphic functions.  ... 
doi:10.1016/j.jmaa.2005.05.038 fatcat:jaj4wdobgzc7bdtvqcu6afqhr4

Normal forms and gauge symmetry of local dynamics

S. L. Lyakhovich, A. A. Sharapov
2009 Journal of Mathematical Physics  
Even though no pairing exists between the constraints and the gauge symmetry generators in general non-variational dynamics, certain counterparts still can be identified of the first- and second-class  ...  For the variational equations, this procedure reduces to the Dirac-Bergmann algorithm for the constrained Hamiltonian systems with certain extension: it remains applicable beyond the scope of Dirac's conjecture  ...  Gorbatenko for illuminating discussions on regularity of analytic varieties.  ... 
doi:10.1063/1.3193684 fatcat:lb5qiq74vnfatpwbg5vbekel6u

On extending the Painlevé test to the one-dimensional Vlasov equation [article]

Piotr P. Goldstein
2018 arXiv   pre-print
The compatibility conditions for the Laurent series have the form of an overdetermined system of 1st order differential equations, which themselves need a compatibility condition.  ...  An analysis of possible extension of the Painlev\'e test, to encompass the one-dimensional Vlasov equation, is performed. The extending requires a nontrivial generalization of the test.  ...  We try a new method which yields classification of meromorphic solutions of the one-dimensional Vlasov-Poisson system and leads to explicit solutions in some simplest cases.  ... 
arXiv:1810.04145v2 fatcat:kt6ufgq4ince3my3unerhe6yqy

Periodic Solutions, Stability and Non-Integrability in a Generalized Hénon-Heiles Hamiltonian System

Dante Carrasco, Claudio Vidal
2013 Journal of Nonlinear Mathematical Physics  
Finally, we show that the generalized Hénon-Heiles systems cannot have any second first integral of class C 1 in the sense of Liouville-Arnol'd.  ...  of nonintegrability of the system associated to H.  ...  The authors would like to acknowledge to the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper.  ... 
doi:10.1080/14029251.2013.805567 fatcat:7pma6ffesjfafjbxx7m5ka4t5y

Non-minimal quasi-holes and topological degeneracy of FQHE [article]

Riccardo Bergamin
2020 arXiv   pre-print
We also discuss the higher genus generalization of the Vafa model of FQHE and the corresponding tt^* geometry.  ...  We extend the analysis of the Vafa N=4 SUSY model of FQHE and discuss other observables which characterize the FQHE topological order.  ...  The choice of the Kahler potential has no influence on the IR dynamics of the quantum system. What is relevant for monodromy considerations is the 1-form dW.  ... 
arXiv:1912.10868v4 fatcat:u27mpjowo5caxock4c2rjfqjom
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