{VERSION 3 0 "IBM INTEL NT" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 226 0 0 0 
0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 558 "cobweb:=proc(g::pro
cedure,x0::numeric,n::posint,c::numeric,d::numeric,a::numeric)\nlocal \+
p1,p2,pts,steps;\nif c>=d then ERROR(`d should be greater than c`, d,c
); fi;\npts:=array(1..4*n+2);\nsteps:=proc(g::procedure,x0::numeric,n:
:posint,c::numeric,d::numeric,a::numeric,pts::array)\nlocal x1,x2,i;\n
x1:=x0;\npts[1]:=x0:pts[2]:=0:\nfor i from 1 to n do\nx2:=g(x1,a);\npt
s[4*i-1]:=x1:pts[4*i]:=x2:pts[4*i+1]:=x2:pts[4*i+2]:=x2:\nx1:=x2;\nod;
\011\nend;\nevalhf(steps(g,x0,n,c,d,a,var(pts)));\np1:=pointplot(op(pt
s),style=LINE):\np2:=plot(\{g(x,a),x\},x=c..d):\ndisplay(\{p1,p2\});\n
end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 628 "newweb:=proc(g::pr
ocedure,x0::numeric,c::numeric,d::numeric,a::numeric,m::posint,n::posi
nt)\nlocal p1,p2,pts,steps;\nif c>=d then ERROR(`d should be greater t
han c`, d,c); fi;\nif m>=n then ERROR(`n should be greater than m`, n,
m); fi;\npts:=array(1..2*(n-m));\nsteps:=proc(g::procedure,x0::numeric
,c::numeric,d::numeric,a::numeric,m::posint,n::posint,pts::array)\nloc
al x1,i; \nx1:=x0;\nfor i from 1 to m do\nx1:=g(x1,a);\nod;\nfor i fro
m 1 to n-m do\nx1:=evalf(g(x1,a));\npts[2*i-1]:=x1:pts[2*i]:=g(x1,a):
\nod;\011\nend;\nevalhf(steps(g,x0,c,d,a,m,n,var(pts)));\np1:=pointplo
t(op(pts),style=LINE):\np2:=plot(g(x,a),x=c..d):\ndisplay(\{p1,p2\});
\nend: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 679 "orbit:=proc(g::
procedure,x0::numeric,c::numeric,d::numeric,r::posint,m::posint,n::pos
int)\nlocal pts,steps;\nif c>=d then ERROR(`d should be greater than c
`, d,c); fi;\nif m>=n then ERROR(`n should be greater than m`, n,m); f
i;\npts:=array(1..2*r*(n-m));\nsteps:=proc(g::procedure,x0::numeric,c:
:numeric,d::numeric,r::posint,m::posint,n::posint,pts::array)\nlocal r
ange,a,x1,i,j;\nrange:=d-c;\nj:=0;\nfor a from c by range/r while abs(
d-a)>0.5e-6 do\nj:=j+1;\nx1:=x0;\nfor i from 1 to m do\nx1:=g(x1,a);\n
od;\nfor i from 1 to n-m do\nx1:=g(x1,a);\npts[(2*i-1)+2*(j-1)*(n-m)]:
=a:pts[2*i+2*(j-1)*(n-m)]:=x1;\nod;\nod;\nend;\nevalhf(steps(g,x0,c,d,
r,m,n,var(pts)));\npointplot(op(pts),style=POINT);\nend: " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 759 "lyapexp:=proc(g::procedure,x0::num
eric,c::numeric,d::numeric,r::posint,m::posint,n::posint)\nlocal dg,pt
s,steps;\nif c>=d then ERROR(`d should be greater than c`, d,c); fi;\n
if m>=n then ERROR(`n should be greater than m`, n,m); fi;\npts:=array
(1..2*r);\ndg:=D[1](g);\nsteps:=proc(g::procedure,dg::procedure,x0::nu
meric,c::numeric,d::numeric,r::posint,m::posint,n::posint,pts::array)
\nlocal range,a,x1,d1,i,j,sum,le;\nrange:=d-c;\nj:=0;\nfor a from c by
 range/r while abs(d-a)>0.5e-6 do\011\nj:=j+1;\nx1:=x0;\nfor i from 1 \+
to m do\nx1:=g(x1,a);\nod;\nsum:=0;\nfor i from 1 to n-m do\nx1:=g(x1,
a);\nd1:=dg(x1,a);\011\011\011\nsum:=sum+ln(abs(d1));\nod;\nle:=sum/(n
-m);\npts[2*j-1]:=a;\npts[2*j]:=le;\nod;\nend;\nevalhf(steps(g,dg,x0,c
,d,r,m,n,var(pts)));\npointplot(op(pts),style=LINE);\nend:         " }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "save `maptools.m`;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "5 0 0" 0 }
{VIEWOPTS 1 1 0 1 1 1803 }