Hamiltonian Chaos

Nondissipative or Hamiltonian systems are also capable of chaos as phase space volume is twisted and folded in area-preserving maps like the Standard Map. When nonintegrable terms are added to a potential function, Hamiltonian chaos emerges. The Standard Map (also known as the Chirikov map) for a periodically kicked rigid rotator provides a simple model with which to explore the emergence of Hamiltonian chaos as well as the KAM theory of islands of stability. A periodically kicked harmonic oscillator displays extended chaos in the web map. Hamiltonian classical chaos makes a direct connection to quantum chaos, which is illustrated using the chaotic stadium, for which quantum scars are associated with periodic classical orbits in the stadium.