TY - JOUR
T1 - Aubry-Mather theory for contact Hamiltonian systems III
AU - Ni, Panrui
AU - Wang, Lin
N1 - Publisher Copyright:
© Science China Press 2024.
PY - 2024/11
Y1 - 2024/11
N2 - By exploiting the contact Hamiltonian dynamics (T* M × ℝ, Φt) around the Aubry set of contact Hamiltonian systems, we provide a relation among the Mather set, the Φt-recurrent set, the strongly static set, the Aubry set, the Mañé set, and the Φt-non-wandering set. Moreover, we consider the strongly static set, as a new flow-invariant set between the Mather set and the Aubry set in the strictly increasing case. We show that this set plays an essential role in the representation of certain minimal forward weak Kolmogorov-Arnold-Moser (KAM) solutions and the existence of transitive orbits around the Aubry set.
AB - By exploiting the contact Hamiltonian dynamics (T* M × ℝ, Φt) around the Aubry set of contact Hamiltonian systems, we provide a relation among the Mather set, the Φt-recurrent set, the strongly static set, the Aubry set, the Mañé set, and the Φt-non-wandering set. Moreover, we consider the strongly static set, as a new flow-invariant set between the Mather set and the Aubry set in the strictly increasing case. We show that this set plays an essential role in the representation of certain minimal forward weak Kolmogorov-Arnold-Moser (KAM) solutions and the existence of transitive orbits around the Aubry set.
KW - 35D40
KW - 35F21
KW - 37J51
KW - Aubry-Mather theory
KW - contact Hamiltonian systems
KW - Hamilton-Jacobi equations
KW - weak KAM theory
UR - http://www.scopus.com/inward/record.url?scp=85196742022&partnerID=8YFLogxK
U2 - 10.1007/s11425-022-2197-4
DO - 10.1007/s11425-022-2197-4
M3 - Article
AN - SCOPUS:85196742022
SN - 1674-7283
VL - 67
SP - 2541
EP - 2570
JO - Science China Mathematics
JF - Science China Mathematics
IS - 11
ER -