Editing Hamiltonian system (section)

=== Characteristics ===
Hamiltonian chaos is characterized by the following features:<ref name="ott" />

'''Sensitivity to Initial Conditions''': A hallmark of chaotic systems, small differences in initial conditions can lead to vastly different trajectories. This is known as the butterfly effect.<ref>{{Cite journal |last=Lorenz |first=Edward N. |date=1963-03-01 |title=Deterministic Nonperiodic Flow |url=https://journals.ametsoc.org/view/journals/atsc/20/2/1520-0469_1963_020_0130_dnf_2_0_co_2.xml |journal=Journal of the Atmospheric Sciences |language=EN |volume=20 |issue=2 |pages=130–141 |doi=10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 |issn=0022-4928|doi-access=free }}</ref>

'''Mixing''': Over time, the phases of the system become uniformly distributed in phase space.<ref>{{Cite book |last=Kornfel'd |first=Isaak P. |title=Ergodic Theory |last2=Fomin |first2=Sergej V. |last3=Sinaj |first3=Jakov G. |date=1982 |publisher=Springer |isbn=978-1-4615-6929-9 |series=Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |location=New York, NY Heidelberg Berlin}}</ref>

'''Recurrence''': Though unpredictable, the system eventually revisits states that are arbitrarily close to its initial state, known as [[Poincaré recurrence theorem|Poincaré recurrence]].

Hamiltonian chaos is also associated with the presence of ''chaotic invariants'' such as the [[Lyapunov exponent]] and [[Kolmogorov-Sinai entropy]], which quantify the rate at which nearby trajectories diverge and the complexity of the system, respectively.<ref name="ott" />