1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
<!--Converted with LaTeX2HTML 98.1p1 release (March 2nd, 1998)
originally by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
* with significant contributions from:
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
<HTML>
<HEAD>
<TITLE>Periodic Variables</TITLE>
<META NAME="description" CONTENT="Periodic Variables">
<META NAME="keywords" CONTENT="userman">
<META NAME="resource-type" CONTENT="document">
<META NAME="distribution" CONTENT="global">
<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1">
<LINK REL="STYLESHEET" HREF="userman.css">
<LINK REL="next" HREF="node37.html">
<LINK REL="previous" HREF="node35.html">
<LINK REL="up" HREF="node34.html">
<LINK REL="next" HREF="node37.html">
</HEAD>
<BODY >
<!--Navigation Panel-->
<A NAME="tex2html992"
HREF="node37.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
SRC="/usr/lib/latex2html/icons.gif/next_motif.gif"></A>
<A NAME="tex2html989"
HREF="node34.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
SRC="/usr/lib/latex2html/icons.gif/up_motif.gif"></A>
<A NAME="tex2html983"
HREF="node35.html">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
SRC="/usr/lib/latex2html/icons.gif/previous_motif.gif"></A>
<A NAME="tex2html991"
HREF="node1.html">
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
SRC="/usr/lib/latex2html/icons.gif/contents_motif.gif"></A>
<BR>
<B> Next:</B> <A NAME="tex2html993"
HREF="node37.html">Initial Conditions and Default</A>
<B> Up:</B> <A NAME="tex2html990"
HREF="node34.html">Defining Dynamical Systems Using</A>
<B> Previous:</B> <A NAME="tex2html984"
HREF="node35.html">Basic Functionality</A>
<BR>
<BR>
<!--End of Navigation Panel-->
<H2><A NAME="SECTION00512000000000000000"> </A><A NAME="1701"> </A>
<BR>
Periodic Variables
</H2>
<P>
Phase space variables may be declared periodic on a fixed interval
by using the PERIODIC command. We define the following map on the
torus,
<!-- MATH: $T^2=\real^2/\zed^2$ -->
59#59:
<P>
<PRE>
# The Kim-Ostlund torus map (kotorus.def)
x' = x + w1 - a / (2 PI) sin(2 PI y)
y' = y + w2 - a / (2 PI) sin(2 PI x)
INITIAL w1 0.6 w2 0.805 a 0.7
PERIODIC x 0 1 y 0 1
</PRE>
<P>
The PERIODIC command should only be given once in the definition
and all periodic variables should be declared, but optionally may be placed
on separate lines.
When trying this example, don't forget to set the dynamical system type
setting to Mapping before selecting ``Build model''.
<P>
<BR><HR>
<ADDRESS>
<I>John Lapeyre</I>
<BR><I>1998-09-04</I>
</ADDRESS>
</BODY>
</HTML>
|
