TY - JOUR
T1 - The essential coexistence phenomenon in Hamiltonian dynamics
AU - Chen, Jianyu
AU - Hu, Huyi
AU - Pesin, Yakov
AU - Zhang, K. E.
N1 - Publisher Copyright:
© 2022 Cambridge University Press. All rights reserved.
PY - 2022/2/8
Y1 - 2022/2/8
N2 - We construct an example of a Hamiltonian flow on a four-dimensional smooth manifold which after being restricted to an energy surface demonstrates essential coexistence of regular and chaotic dynamics, that is, there is an open and dense-invariant subset such that the restriction has non-zero Lyapunov exponents in all directions (except for the direction of the flow) and is a Bernoulli flow while, on the boundary, which has positive volume, all Lyapunov exponents of the system are zero.
AB - We construct an example of a Hamiltonian flow on a four-dimensional smooth manifold which after being restricted to an energy surface demonstrates essential coexistence of regular and chaotic dynamics, that is, there is an open and dense-invariant subset such that the restriction has non-zero Lyapunov exponents in all directions (except for the direction of the flow) and is a Bernoulli flow while, on the boundary, which has positive volume, all Lyapunov exponents of the system are zero.
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U2 - 10.1017/etds.2021.13
DO - 10.1017/etds.2021.13
M3 - Article
AN - SCOPUS:85105321301
SN - 0143-3857
VL - 42
SP - 592
EP - 613
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 2
ER -