Fitting Invariant Curves on Billiard Tables and the Birkhoff-Herman Theorem

2004 ◽  
pp. 29-36
Author(s):  
Edoh Y. Amiran
Keyword(s):  
Invariant Curves

On quasi-invariant curves

Astérisque ◽  
2020 ◽  
Vol 416 ◽  
pp. 181-191
Author(s):  
Ricardo PEREZ-MARCO
Keyword(s):  
Invariant Curves

Invariant curves for area-preserving twist maps far from integrable

1991 ◽  
Vol 65 (3-4) ◽  
pp. 617-643 ◽  
Author(s):  
Alessandra Celletti ◽  
Luigi Chierchia
Keyword(s):  
Invariant Curves ◽  
Twist Maps ◽  
Area Preserving

Invariant curves for variable step size integrators

1991 ◽  
Vol 31 (1) ◽  
pp. 169-180 ◽  
Author(s):  
Daniel Stoffer ◽  
Kaspar Nipp
Keyword(s):  
Variable Step Size ◽  
Invariant Curves ◽  
Step Size ◽  
Variable Step

Invariant Curves for Mappings

1986 ◽  
Vol 17 (5) ◽  
pp. 1053-1067 ◽  
Author(s):  
Hal L. Smith
Keyword(s):  
Invariant Curves

scholarly journals The non-hyperbolicity of irrational invariant curves for twist maps and all that follows

2016 ◽  
Vol 32 (4) ◽  
pp. 1295-1310 ◽  
Author(s):  
Marie-Claude Arnaud ◽  
Pierre Berger
Keyword(s):  
Invariant Curves ◽  
Twist Maps

scholarly journals Analytic invariant curves for a planar map

2002 ◽  
Vol 15 (5) ◽  
pp. 567-573 ◽  
Author(s):  
Jian-Guo Si ◽  
Xin-Ping Wang ◽  
Wei-Nian Zhang
Keyword(s):  
Invariant Curves ◽  
Planar Map ◽  
Analytic Invariant

scholarly journals The Lagrangian Stability for a Class of Second-Order Quasi-Periodic Reversible Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Yanling Shi ◽  
Jia Li
Keyword(s):  
Differential Equation ◽  
Analytic Functions ◽  
Order Differential Equation ◽  
Reversible Systems ◽  
Invariant Curves ◽  
Real Analytic Functions ◽  
All Solutions ◽  
Small Twist Theorem ◽  
Real Analytic ◽  
Twist Theorem

We study the following two-order differential equation,(Φp(x'))'+f(x,t)Φp(x')+g(x,t)=0,whereΦp(s)=|s|(p-2)s,p>0.f(x,t)andg(x,t)are real analytic functions inxandt,2aπp-periodic inx, and quasi-periodic intwith frequencies(ω1,…,ωm). Under some odd-even property off(x,t)andg(x,t), we obtain the existence of invariant curves for the above equations by a variant of small twist theorem. Then all solutions for the above equations are bounded in the sense ofsupt∈R|x′(t)|<+∞.

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