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Global Results for Weakly Dispersive KP-II Equations on the Cylinder. [PDF]
Arch Ration Mech AnalHerr S, Schippa R, Tzvetkov N.
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BIFURCATIONS ON ELLIPTIC FUNCTIONS
International Journal of Bifurcation and Chaos, 2001In this paper we are dealing with the dynamical properties of the Jacobian elliptic functions, cosine-amplitude and sine-amplitude. Seen as one parameter dynamical systems, they present a flip type bifurcation at the origin. In fact they are particular cases of some general families of functions holding sufficient conditions we call degenerate.
Francisco Balibrea +2 more
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On the Definitions of Elliptic Functions
The Mathematical Gazette, 1944In practice it is generally as inverse functions of elliptic integrals that elliptic functions are needed; and so a simple demonstration of this important property of the functions is to be desired. The important step in such a demonstration is a proof that the inverse of an elliptic integral is a one-valued function, which for every value of the ...
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On Factorization of Elliptic Functions
Canadian Journal of Mathematics, 1968In this paper we shall be concerned with the following problem: If h is an elliptic function and h(z) = ƒ(g(z)), what can be said about the functions ƒ and g? In order to simplify the discussion we introduce some basic definitions.Definition 1. A meromorphic function h(z) = ƒ(g(z)) is said to have ƒ(z) and g(z) as left and right factors, respectively ...
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Elliptic integrals, theta functions and elliptic functions
1966General remarks. Any integral of the type ∫ R \(\left( {z,{Z^{\frac{1}{2}}}} \right)\) is a rational function of x and y and Z is a polynomial of the third or fourth degree in z with real coefficients and no repeated factors is called an elliptic integral.
Wilhelm Magnus +2 more
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2001
In its first six chapters this 2006 text seeks to present the basic ideas and properties of the Jacobi elliptic functions as an historical essay, an attempt to answer the fascinating question: 'what would the treatment of elliptic functions have been like if Abel had developed the ideas, rather than Jacobi?' Accordingly, it is based on the idea of ...
J. V. Armitage, W. F. Eberlein
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In its first six chapters this 2006 text seeks to present the basic ideas and properties of the Jacobi elliptic functions as an historical essay, an attempt to answer the fascinating question: 'what would the treatment of elliptic functions have been like if Abel had developed the ideas, rather than Jacobi?' Accordingly, it is based on the idea of ...
J. V. Armitage, W. F. Eberlein
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Elliptic Functions and Elliptic Curves
1973A comprehensive treatment of elliptic functions is linked by these notes to a study of their application to elliptic curves. This approach provides geometers with the opportunity to acquaint themselves with aspects of their subject virtually ignored by other texts.
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