4.2 The Complete Ternary Horseshoe
105
Fig. 4.2 Mapping for T = 5.
(a) Ternary horseshoe at
level 0. (b) Ternary horseshoe
at level 1 (after one kick). (c)
Ternary horseshoe up to level
2 (after two kicks) (plots by
Christof Jung)
In Fig. 4.4, we show two mappings of the stable and unstable manifolds in
Fig. 4.2a, one that goes forward in time and another that goes backward in time.
The mapping is completely symmetric in these two time directions. As we continue
mapping the system (forward in time and backward in time), the tendrils formed by
the original stable and unstable manifolds in Fig. 4.2a stretch and fold further and
further out into the asymptotic region (both forward in time and backward in time).