TY - JOUR
T1 - The Spectrum of Period-Doubling Hamiltonian
AU - Liu, Qinghui
AU - Qu, Yanhui
AU - Yao, Xiao
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2022/9
Y1 - 2022/9
N2 - In this paper, we show the following: the Hausdorff dimension of the spectrum of period-doubling Hamiltonian is bigger than log α/ log 4 , where α is the Golden number; there exists a dense uncountable subset of the spectrum such that for each energy in this set, the related trace orbit is unbounded, which is in contrast with a recent result of Carvalho (Nonlinearity 33, 2020); we give a complete characterization for the structure of gaps and the gap labelling of the spectrum. All of these results are consequences of an intrinsic coding of the spectrum we construct in this paper.
AB - In this paper, we show the following: the Hausdorff dimension of the spectrum of period-doubling Hamiltonian is bigger than log α/ log 4 , where α is the Golden number; there exists a dense uncountable subset of the spectrum such that for each energy in this set, the related trace orbit is unbounded, which is in contrast with a recent result of Carvalho (Nonlinearity 33, 2020); we give a complete characterization for the structure of gaps and the gap labelling of the spectrum. All of these results are consequences of an intrinsic coding of the spectrum we construct in this paper.
UR - http://www.scopus.com/inward/record.url?scp=85131512152&partnerID=8YFLogxK
U2 - 10.1007/s00220-022-04417-7
DO - 10.1007/s00220-022-04417-7
M3 - Article
AN - SCOPUS:85131512152
SN - 0010-3616
VL - 394
SP - 1039
EP - 1100
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 3
ER -