Chapter 1: Abstract Scheme for Obtaining Higher-Order Conditions in Smooth Extremal Problems with Constraints

2012 ◽  
pp. 9-25
Keyword(s):  
Extremal Problems ◽  
Higher Order ◽  
Order Conditions

scholarly journals Stratifications of equivariant varieties

1977 ◽  
Vol 16 (2) ◽  
pp. 279-295 ◽  
Author(s):  
M.J. Field
Keyword(s):  
Lie Group ◽  
General Position ◽  
Higher Order ◽  
Order Conditions ◽  
Compact Lie Group ◽  
Algebraic Varieties ◽  
Equivariant Maps

Let G be a compact Lie group and V and W be linear G spaces. A study is made of the canonical stratification of some algebraic varieties that arise naturally in the theory of C∞ equivariant maps from V to W. The main corollary of our results is the equivalence of Bierstone's concept of “equivariant general position” with our own of “G transversal”. The paper concludes with a description of Bierstone's higher order conditions for equivariant maps in the framework of equisingularity sequences.

Higher-order conditions for singular Lagrangian dynamics

1992 ◽  
Vol 25 (7) ◽  
pp. 1989-2004 ◽  
Author(s):  
X Gracia ◽  
J M Pons ◽  
N Roman-Roy
Keyword(s):  
Higher Order ◽  
Order Conditions ◽  
Lagrangian Dynamics

scholarly journals Local bifurcations of continuous dynamical systems under higher order conditions

2010 ◽  
Vol 23 (3) ◽  
pp. 230-234 ◽  
Author(s):  
F. Balibrea ◽  
A. Martinez ◽  
Jose C. Valverde
Keyword(s):  
Dynamical Systems ◽  
Higher Order ◽  
Order Conditions ◽  
Local Bifurcations
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