jordan system
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2019 ◽  
Vol 32 (03) ◽  
pp. 2050006
Author(s):  
B. G. Konopelchenko ◽  
G. Ortenzi

Singularities of plane into plane mappings described by parabolic two-component systems of quasi-linear partial differential equations of the first order are studied. Impediments arising in the application of the original Whitney’s approach to such a case are discussed. Hierarchy of singularities is analyzed by the double-scaling expansion method for the simplest [Formula: see text]-component Jordan system. It is shown that flex is the lowest singularity while higher singularities are given by [Formula: see text] curves which are of cusp type for [Formula: see text], [Formula: see text] Regularization of these singularities by deformation of plane into plane mappings into surface [Formula: see text] to plane is discussed. Applicability of the proposed approach to other parabolic type mappings is noted. We finally compare the results obtained for the parabolic case with non-generic gradient catastrophes for hyperbolic systems.



Author(s):  
José A. Anquela ◽  
Teresa Cortés ◽  
Efim Zelmanov
Keyword(s):  


2016 ◽  
Vol 292 (1) ◽  
pp. 1-9
Author(s):  
José A. Anquela ◽  
Teresa Cortés ◽  
Efim Zelmanov
Keyword(s):  


2002 ◽  
Vol 172 (2-3) ◽  
pp. 119-137 ◽  
Author(s):  
José A. Anquela ◽  
Teresa Cortés ◽  
Esther Garcı́a
Keyword(s):  


2001 ◽  
Vol 106 (3) ◽  
pp. 279-290 ◽  
Author(s):  
Jos� A. Anquela ◽  
Teresa Cort�s ◽  
Esther Garc�a
Keyword(s):  


1993 ◽  
Vol 114 (1) ◽  
pp. 149-161 ◽  
Author(s):  
Ottmar Loos

The two main results of this paper are:(i) The set of properly algebraic elements of a Jordan system (algebra, triple system or pair) over an uncountable field is an ideal.(ii) For a semiprimitive Banach Jordan system, the socle, the largest properly algebraic ideal, the largest properly spectrum-finite ideal and the largest von Neumann regular ideal all coincide.



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