A Strong Inverse Function Theorem

1988 ◽  
Vol 95 (7) ◽  
pp. 648-651
Author(s):  
William J. Knight
Keyword(s):  
Inverse Function ◽  
Inverse Function Theorem

scholarly journals Normal forms for perturbations of systems possessing a Diophantine invariant torus

2017 ◽  
Vol 39 (8) ◽  
pp. 2176-2222 ◽  
Author(s):  
JESSICA ELISA MASSETTI
Keyword(s):  
Vector Fields ◽  
Normal Forms ◽  
Invariant Tori ◽  
Inverse Function ◽  
Hamiltonian Mechanics ◽  
Inverse Function Theorem ◽  
Unified Framework ◽  
Normal Form Theorem ◽  
Real Analytic ◽  
Twist Theorem

We give a new proof of Moser’s 1967 normal-form theorem for real analytic perturbations of vector fields possessing a reducible Diophantine invariant quasi-periodic torus. The proposed approach, based on an inverse function theorem in analytic class, is flexible and can be adapted to several contexts. This allows us to prove in a unified framework the persistence, up to finitely many parameters, of Diophantine quasi-periodic normally hyperbolic reducible invariant tori for vector fields originating from dissipative generalizations of Hamiltonian mechanics. As a byproduct, generalizations of Herman’s twist theorem and Rüssmann’s translated curve theorem are proved.

scholarly journals About a local approximation theorem and an inverse function theorem

1980 ◽  
Vol 22 (2) ◽  
pp. 185-192 ◽  
Author(s):  
J. W. Nieuwenhuis
Keyword(s):  
Approximation Theorem ◽  
Inverse Function ◽  
Local Approximation ◽  
Inverse Function Theorem ◽  
Short Route

AbstractThis paper gives a theorem by which it is possible to derive in an easy way a local approximation theorem and an inverse function theorem. The latter theorems are not new. The main advantage of our paper is in giving a relatively short route to these results.

scholarly journals Differentiable retracts and a modified inverse function theorem

1978 ◽  
Vol 18 (1) ◽  
pp. 37-43 ◽  
Author(s):  
W. Barit ◽  
G.R. Wood
Keyword(s):  
Inverse Function ◽  
Weak Version ◽  
Inverse Function Theorem ◽  
Infinite Dimensional ◽  
Counter Example ◽  
Finite Dimensional

A lemma is presented which is a weak version of the inverse function theorem, in that differentiability is assumed instead of continuous differentiability. The result holds only for finite dimensional spaces; a counter-example is given for the infinite dimensional analogue. The lemma is used to answer a question posed by Nadler concerning differentiable retracts.

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