scholarly journals ON THE REPRESENTATION OF MAPS BY LIE TRASFORMS

2012 ◽  
Author(s):  
Antonio Giorgilli
Keyword(s):  
Normal Form ◽  
Arbitrary Dimension ◽  
Lie Series ◽  
Straightforward Manner ◽  
Standard Map ◽  
Lie Transform ◽  
Normal Form Methods

The problem of representing a class of maps in a form suited for application of normal form methods is revisited. It is shown that using the methods of Lie series and of Lie transform a normal form algorithm is constructed in a straightforward manner. The examples of the Schröder–Siegel map and of the Chirikov standard map are included, with extension to arbitrary dimension.

Normal form for librational curves of the standard map

Meccanica ◽  
1995 ◽  
Vol 30 (3) ◽  
pp. 251-260 ◽  
Author(s):  
Alessandra Celletti
Keyword(s):  
Normal Form ◽  
Standard Map ◽  
Librational Curves

Lie Transform Construction of Exponential Normal Form Observers

2003 ◽  
Vol 36 (11) ◽  
pp. 97-102 ◽  
Author(s):  
Suba Thomas ◽  
Harry G. Kwatny ◽  
Bor-Chin Chang
Keyword(s):  
Normal Form ◽  
Lie Transform

scholarly journals Application of Power Geometry and Normal Form Methods to the Study of Nonlinear ODEs

2018 ◽  
Vol 173 ◽  
pp. 01004 ◽  
Author(s):  
Victor Edneral
Keyword(s):  
Normal Form ◽  
Closed Form ◽  
Polynomial Systems ◽  
First Integrals ◽  
Degenerate System ◽  
Integrals Of Motion ◽  
Nonlinear Odes ◽  
Power Transformations ◽  
Normal Form Methods ◽  
Power Geometry

This paper describes power transformations of degenerate autonomous polynomial systems of ordinary differential equations which reduce such systems to a non-degenerative form. Example of creating exact first integrals of motion of some planar degenerate system in a closed form is given.

Closing the GAP—A 5Å Scanning Microscope

1969 ◽  
Vol 27 ◽  
pp. 6-7
Author(s):  
A. V. Crewe
Keyword(s):  
Normal Form ◽  
The Other ◽  
Resolving Power ◽  
Scanning Microscope ◽  
Conventional Microscope ◽  
Other Hand ◽  
Closing The Gap ◽  
Thermal Sources ◽  
Better Than ◽  
Transmission Microscope

We have become accustomed to differentiating between the scanning microscope and the conventional transmission microscope according to the resolving power which the two instruments offer. The conventional microscope is capable of a point resolution of a few angstroms and line resolutions of periodic objects of about 1Å. On the other hand, the scanning microscope, in its normal form, is not ordinarily capable of a point resolution better than 100Å. Upon examining reasons for the 100Å limitation, it becomes clear that this is based more on tradition than reason, and in particular, it is a condition imposed upon the microscope by adherence to thermal sources of electrons.

METHODS OF REDUCING OF LARGE BOOLEAN FORMULAS REPRESENTED IN A CONJUNCTIVE NORMAL FORM FOR DETERMINING THEIR SATISFIABILITY

2020 ◽  
Author(s):  
N.I. Gdansky ◽  
◽  
A.A. Denisov ◽  
Keyword(s):  
Normal Form ◽  
Normal Forms ◽  
Conjunctive Normal Form ◽  
Boolean Formulas

The article explores the satisfiability of conjunctive normal forms used in modeling systems.The problems of CNF preprocessing are considered.The analysis of particular methods for reducing this formulas, which have polynomial input complexity is given.

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