scholarly journals Singularity confinement and full-deautonomisation: A discrete integrability criterion

2015 ◽  
Vol 313 ◽  
pp. 11-25 ◽  
Author(s):  
B. Grammaticos ◽  
A. Ramani ◽  
R. Willox ◽  
T. Mase ◽  
J. Satsuma
Keyword(s):  
Singularity Confinement ◽  
Integrability Criterion

scholarly journals Singularity confinement as an integrability criterion

2019 ◽  
Vol 52 (20) ◽  
pp. 205201 ◽  
Author(s):  
Takafumi Mase ◽  
Ralph Willox ◽  
Alfred Ramani ◽  
Basil Grammaticos
Keyword(s):  
Singularity Confinement ◽  
Integrability Criterion

Square Integrable Representations and the Standard Module Conjecture for General Spin Groups

2009 ◽  
Vol 61 (3) ◽  
pp. 617-640 ◽  
Author(s):  
Wook Kim
Keyword(s):  
Half Plane ◽  
Spin Groups ◽  
Standard Module ◽  
Square Integrability ◽  
Integrability Criterion

Abstract.In this paper we study square integrable representations and L -functions for quasisplit general spin groups over a p-adic field. In the first part, the holomorphy of L -functions in a half plane is proved by using a variant formof Casselman's square integrability criterion and the Langlands–Shahidi method. The remaining part focuses on the proof of the standard module conjecture. We generalize Muić's idea via the Langlands–Shahidimethod towards a proof of the conjecture. It is used in the work of M. Asgari and F. Shahidi on generic transfer for general spin groups.

scholarly journals Singularity Confinement and Chaos in Discrete Systems

1998 ◽  
Vol 81 (2) ◽  
pp. 325-328 ◽  
Author(s):  
Jarmo Hietarinta ◽  
Claude Viallet
Keyword(s):  
Discrete Systems ◽  
Singularity Confinement

scholarly journals The Gauge Integral Theory in HOL4

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Zhiping Shi ◽  
Weiqing Gu ◽  
Xiaojuan Li ◽  
Yong Guan ◽  
Shiwei Ye ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Higher Order ◽  
Integral Theory ◽  
Order Logic ◽  
Cauchy Type ◽  
Lebesgue Integral ◽  
Higher Order Logic ◽  
Riemann Integral ◽  
Integrability Criterion ◽  
Class Of Functions

The integral is one of the most important foundations for modeling dynamical systems. The gauge integral is a generalization of the Riemann integral and the Lebesgue integral and applies to a much wider class of functions. In this paper, we formalize the operational properties which contain the linearity, monotonicity, integration by parts, the Cauchy-type integrability criterion, and other important theorems of the gauge integral in higher-order logic 4 (HOL4) and then use them to verify an inverting integrator. The formalized theorem library has been accepted by the HOL4 authority and will appear in HOL4 Kananaskis-9.

scholarly journals Singularity confinement and algebraic integrability

2004 ◽  
Vol 45 (3) ◽  
pp. 1191-1208 ◽  
Author(s):  
S. Lafortune ◽  
A. Goriely
Keyword(s):  
Algebraic Integrability ◽  
Singularity Confinement

scholarly journals On an integrability criterion for a family of cubic oscillators

2021 ◽  
Vol 6 (11) ◽  
pp. 12902-12910
Author(s):  
Dmitry Sinelshchikov ◽  
Keyword(s):  
Canonical Form ◽  
Irreducible Polynomial ◽  
First Integral ◽  
Nonlinear Oscillators ◽  
Invariant Curves ◽  
Polynomial Invariant ◽  
Equivalence Transformations ◽  
First Derivative ◽  
Equivalence Criterion ◽  
Integrability Criterion

<abstract><p>In this work we consider a family of cubic, with respect to the first derivative, nonlinear oscillators. We obtain the equivalence criterion for this family of equations and a non-canonical form of Ince Ⅶ equation, where as equivalence transformations we use generalized nonlocal transformations. As a result, we construct two integrable subfamilies of the considered family of equations. We also demonstrate that each member of these two subfamilies possesses an autonomous parametric first integral. Furthermore, we show that generalized nonlocal transformations preserve autonomous invariant curves for the equations from the studied family. As a consequence, we demonstrate that each member of these integrable subfamilies has two autonomous invariant curves, that correspond to irreducible polynomial invariant curves of the considered non-canonical form of Ince Ⅶ equation. We illustrate our results by two examples: An integrable cubic oscillator and a particular case of the Liénard (4, 9) equation.</p></abstract>

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