TY - JOUR
T1 - QUANTITATIVE DESTRUCTION OF INVARIANT CIRCLES
AU - Wang, Lin
N1 - Publisher Copyright:
© 2022 American Institute of Mathematical Sciences. All rights reserved.
PY - 2022/3
Y1 - 2022/3
N2 - For area-preserving twist maps on the annulus, we consider the problem on quantitative destruction of invariant circles with a given frequency ω of an integrable system by a trigonometric polynomial of degree N perturbation RNwith ||RN||Cr< ϵ. We obtain a relation among N, r, ϵ and the arithmetic property of ω, for which the area-preserving map admit no invariant circles with ω.
AB - For area-preserving twist maps on the annulus, we consider the problem on quantitative destruction of invariant circles with a given frequency ω of an integrable system by a trigonometric polynomial of degree N perturbation RNwith ||RN||Cr< ϵ. We obtain a relation among N, r, ϵ and the arithmetic property of ω, for which the area-preserving map admit no invariant circles with ω.
KW - Invariant circle
KW - Minimal configuration
KW - Peierls's barrier
KW - Trigonometric polynomial
UR - https://www.scopus.com/pages/publications/85124536948
U2 - 10.3934/dcds.2021164
DO - 10.3934/dcds.2021164
M3 - Article
AN - SCOPUS:85124536948
SN - 1078-0947
VL - 42
SP - 1569
EP - 1583
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
IS - 3
ER -