scholarly journals A sharpened form of the inverse function theorem

2020 ◽  
Vol 73 (2) ◽  
pp. 59
Author(s):  
Mark Elin ◽  
David Shoikhet
Keyword(s):  
Numerical Range ◽  
Inverse Function ◽  
Inverse Function Theorem ◽  
Geometrical Properties ◽  
Hyperbolic Convexity ◽  
Advanced Version ◽  
Sharpened Form

In this note we establish an advanced version of the inverse function theorem and study some local geometrical properties like starlikeness and hyperbolic convexity of the inverse function under natural restrictions on the numerical range of the underlying mapping.

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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