1
2
(x,y,u)
u
3
4
A transient behavior
5
long periodic orbit, θ= π/4, a=0.05535, b=0.08775
6tan(θ) = 1, a/b irrational, recurrent, ergodic
7Tan(θ) = 3, 1000 reflections
Recurrent, ergodic
8tan(θ) = 3, 3000 reflections
9
10
11
12
13
14
15
BA
D C
B1
16
A B
D C
B1
C1
A1
D1
17
18
19
A B
D C
B1
C1
A1
D1
20
21
22
23
24
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