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MEE 201 Advanced Dynamics.
11/15/2007.
Homework set No. 5
Due Wednesday, 11/22/2007 in class.
1. Consider the standard map studied in class.
I
0
=
I
+
δ
sin(2
πϕ
)
,
ϕ
0
=
ϕ
+
I
+
δ
sin(2
πϕ
)
,
Study the change of the phase space of the standard map as
δ
changes
from 0 to 2
π
. Speciﬁcally, plot the cases of
δ
= 0
.
2
/
2
π,
0
.
6
/
2
/pi.
1
/
2
π
and
δ
= 2
π
. Describe your investigation.
2. Find the criterion for existence of 1
/
2 periodic orbit of the standard map
(hint: study the second iterate of the map). Compare your analytical
criterion with what you see n the numerical phase portrait for small
δ <
1
/
2
π
. What happens close to that trajectory as
δ
is increased?
3. Study the standard map with dissipation
I
0
= (1

γ
)
I
+
δ
sin(2
πϕ
)
,
ϕ
0
=
ϕ
+
I
+
δ
sin(2
πϕ
)
,
where
γ
is small (in the range 0
,
0
.
5). Which changes do you expect in
the phase portrait from the conservative case? Plot characteristic phase
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This note was uploaded on 08/06/2010 for the course ME 201 taught by Professor Mezic,i during the Fall '08 term at UCSB.
 Fall '08
 Mezic,I

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