Symbolic Dynamics & Shift Maps
Map:
Tent map (2-shift)
Logistic map r=4
Doubling map (angle)
Baker's map
Initial x₀
0.123
Partition threshold
0.50
Steps
80
Animate Shift
New IC
σ(s₀s₁s₂…) = s₁s₂s₃…
Shift map encodes orbits
Sensitive dep: two nearby
orbits diverge in symbol space
Entropy h = log₂(alphabet size)
Symbolic dynamics · shift homeomorphism · topological entropy · Smale horseshoe