An Introduction To Small Divisors Problems

1992 ◽  
pp. 659-679 ◽  
Author(s):  
Jean-Christophe Yoccoz
Keyword(s):  
Small Divisors

scholarly journals Diophantine conditions in small divisors and transcendental number theory

2003 ◽  
Vol 9 (6) ◽  
pp. 1401-1409
Author(s):  
E. Muñoz Garcia ◽  
◽  
R. Pérez-Marco ◽  
Keyword(s):  
Number Theory ◽  
Transcendental Number ◽  
Small Divisors

On the Parity of the Number of Small Divisors of n

2015 ◽  
pp. 93-100
Author(s):  
Kevin Ford ◽  
Florian Luca ◽  
Carl Pomerance ◽  
Jeffrey Shallit
Keyword(s):  
Small Divisors

scholarly journals A remark on small divisors problems

1978 ◽  
Vol 28 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Hana Petzeltová ◽  
Pavla Vrbová
Keyword(s):  
Small Divisors

scholarly journals The existence of Siegel disks for the Cremona map

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2705-2712
Author(s):  
Yong-Guo Shi ◽  
Qian Zhang
Keyword(s):  
Functional Equation ◽  
Analytic Solutions ◽  
Small Divisors ◽  
Brjuno Condition

This paper is concerned with the existence of Siegel disks of the Cremona map F?(x,y)=(x cos?-(y-x2) sin?, x sin?+(y-x2) cos?) with the parameter ? ? [0, 2?). This problem is reduced to the existence of local invertible analytic solutions to a functional equation with small divisors ?n + ?-n - ? - ?-1. The main aim of this paper is to investigate whether this equation with |?|=1 has such a solution under the Brjuno condition.

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