86
3 Area-Preserving Maps
Fig. 3.24 Strobe plots of the
phase space for the paradigm
Hamiltonian for the case
ν α = 1, U
(0)
α = U
(1)
α : (a)
S = 0.48; (b) S = 0.72 (Plots
by Chiu Liu)
well-developed chaotic sea present in this plot. The simple Chirikov criterion does
not take into account the existence of the secondary islands and their contribution.
In fact, there is a whole self-similar hierarchy of resonances that contribute to
the destruction of the last KAM torus, as we have seen in previous sections. The
renormalization procedure developed by Escande and Doveil is able to account for
them.
3 Area-Preserving Maps
Fig. 3.24 Strobe plots of the
phase space for the paradigm
Hamiltonian for the case
ν α = 1, U
(0)
α = U
(1)
α : (a)
S = 0.48; (b) S = 0.72 (Plots
by Chiu Liu)
well-developed chaotic sea present in this plot. The simple Chirikov criterion does
not take into account the existence of the secondary islands and their contribution.
In fact, there is a whole self-similar hierarchy of resonances that contribute to
the destruction of the last KAM torus, as we have seen in previous sections. The
renormalization procedure developed by Escande and Doveil is able to account for
them.