Decay of quasibounded classical Hamiltonian systems and their internal dynamics

Decay of classical chaotic systems: The case of the Bunimovich stadium

“…Again these orbits are responsible for the algebraically delayed escape of particles from fully chaotic systems. This emerges from the arguments of [14] and the numerical experiments of [13] and the present note. Hence, all these phenomena are related to each other.…”

“…The algebraic tail of P (L) and its suppression in the limit of vanishing size ∆ of the hole -briefly the almost exponential decay -is semiquantitatively reproduced by the model inspired by [13] and described in Sec. IV.…”

“…More precisely, the bouncing ball orbits are a set of parabolic [20], non-isolated periodic orbits. A similar set of periodic orbits exists in the Sinai billiard and causes similar effects [13].…”

“…The following schematic model -inspired by the treatment of the Sinai billiard in [13] -shows how the algebraically delayed decay comes about. Suppose that the phase space can be split into two parts C and L such that the decay happens in C, the delay in L. Once the particle is in C, it shall escape with probability ω or immediately go back to L with probability 1 − ω.…”

“…Such regions of phase space have been described e.g. in [10][11][12][13][14][15] and the first Ref. of [2]: Close to the family of bouncing ball orbits and the "whispering gallery orbits" there are parts of phase space with volume > 0 in which the particles can be trapped for an arbitrarily long time.…”