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1 0 bop 692 872 a Fx(Accessible)46 b(P)l(oin)l(ts)e(in)g(the)g(Julia)h
(Sets)e(of)g(Stable)1575 1054 y(Exp)t(onen)l(tials)1498
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(Dev)-5 b(aney)2369 1375 y Fv(\003)1581 1528 y Fw(R.)32
b(E.)h(Lee)h(Deville)1642 1644 y(Kre)-5 b(\024)-44 b(simir)31
b(Josi)m(\023)-46 b(c)1464 1760 y(Monica)32 b(Moreno-Ro)s(c)m(ha)1563
1876 y Fu(Boston)i(University)1607 2071 y Fw(Jan)m(uary)g(5,)e(2001)515
2546 y Ft(1)134 b(In)l(tro)t(duction)515 2728 y Fs(Our)28
b(goal)g(in)h(this)g(pap)r(er)g(is)f(to)h(in)n(v)n(estigate)f(the)h
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b(Our)24 b(goal)f(in)i(this)515 623 y(pap)r(er)i(is)g(to)g(describ)r(e)
g(precisely)g(this)g(set)h(of)f(accessible)f(p)r(oin)n(ts.)37
b(This)27 b(in)h(turn)f(yields)g(a)515 722 y(go)r(o)r(d)g(picture)g(of)
h(the)g(top)r(ology)e(of)i(this)g(set.)639 822 y(T)-7
b(o)20 b(describ)r(e)h(the)g(set)f(of)h(accessible)e(p)r(oin)n(ts,)j(w)
n(e)e(mak)n(e)g(use)h(of)f(the)h Fo(kne)l(ading)j(se)l(quenc)l(e)515
922 y Fs(for)31 b Fr(E)707 934 y Fq(\025)783 922 y Fs(as)g(in)n(tro)r
(duced)h(in)g([6])g(and)g([13)o(].)50 b(W)-7 b(e)33 b(recall)e(this)h
(construction)f(in)h(Section)g(3.)515 1021 y(W)-7 b(e)40
b(review)g(the)h(de\014nition)f(of)g(a)g Fo(str)l(aight)i(brush)f
Fs(and)f(sev)n(eral)e(c)n(haracteristics)g(of)i(a)515
1121 y(Can)n(tor)f(b)r(ouquet)i(in)g(Section)f(4.)76
b(In)40 b([8])h(it)g(is)f(sho)n(wn)g(that)h(p)r(oin)n(ts)f(in)h
Fr(J)8 b Fs(\()p Fr(E)3111 1133 y Fq(\025)3155 1121 y
Fs(\))41 b Fo(with)515 1220 y(b)l(ounde)l(d)22 b(itiner)l(ary)28
b Fs(lie)19 b(on)h(hairs.)33 b(Since)19 b(our)g(result)g(applies)g
(equally)g(w)n(ell)g(to)g(p)r(oin)n(ts)h(with)515 1320
y(un)n(b)r(ounded)27 b(itinerary)-7 b(,)26 b(w)n(e)h(extend)g(this)h
(result)e(to)h(the)h(un)n(b)r(ounded)f(case)f(in)h(Section)g(5.)515
1420 y(Finally)-7 b(,)27 b(in)h(Section)g(6,)f(w)n(e)g(pro)n(v)n(e)f
(accessibilit)n(y)-7 b(.)515 1694 y Ft(2)134 b(Basins)45
b(of)h(A)l(ttraction)515 1876 y Fs(In)33 b(this)h(section)f(w)n(e)g
(will)g(describ)r(e)g(some)g(general)f(prop)r(erties)g(of)h(the)h
(complemen)n(t)f(of)515 1976 y(the)26 b(Julia)g(b)n(y)g(summarizing)f
(some)h(of)g(the)h(results)e(in)i([6)o(].)37 b(W)-7 b(e)27
b(assume)e(that)i Fr(E)3075 1988 y Fq(\025)3145 1976
y Fs(has)e(an)515 2075 y(attracting)k(p)r(erio)r(dic)h(cycle)f
Fr(z)1472 2087 y Fp(0)1509 2075 y Fr(;)14 b(:::;)g(z)1691
2087 y Fq(n)1763 2075 y Fs(=)27 b Fr(z)1894 2087 y Fp(0)1961
2075 y Fs(of)i(prime)h(p)r(erio)r(d)g Fr(n)p Fs(,)h(with)f
Fr(E)2912 2087 y Fq(\025)2956 2075 y Fs(\()p Fr(z)3027
2087 y Fq(i)3055 2075 y Fs(\))d(=)g Fr(z)3245 2087 y
Fq(i)p Fp(+1)3356 2075 y Fs(.)515 2175 y(Throughout)i(w)n(e)h(assume)f
(that)i Fr(n)c Fn(\025)g Fs(2.)45 b(Let)30 b Fr(A)2068
2145 y Fl(\003)2107 2175 y Fs(\()p Fr(z)2178 2187 y Fq(i)2205
2175 y Fs(\))h(denote)f(the)h(immediate)f(basin)g(of)515
2275 y(attraction)c(con)n(taining)h Fr(z)1345 2287 y
Fq(i)1372 2275 y Fs(.)515 2441 y Fi(De\014nition)33 b(2.1.)41
b Fo(A)n(n)31 b(unb)l(ounde)l(d,)h(simply)h(c)l(onne)l(cte)l(d)f(set)f
Fr(F)39 b Fn(\032)26 b Fm(C)52 b Fo(is)32 b(c)l(al)t(le)l(d)h(a)39
b Fs(\014nger)515 2540 y Fo(of)30 b(width)h Fr(c)f Fo(if)515
2723 y Fi(i\))41 b Fr(F)h Fo(is)30 b(b)l(ounde)l(d)g(by)g(a)g(simple)h
(curve)f Fr(\015)d Fn(\032)c Fm(C)15 b Fo(.)515 2889
y Fi(ii\))40 b Fo(Ther)l(e)25 b(exists)f(a)h Fr(\027)j(>)23
b Fs(0)g Fo(such)i(that)f Fr(F)18 b Fn(\\)6 b(f)p Fr(z)17
b Fn(j)d Fo(R)l(e)f Fr(z)27 b(>)22 b(\027)5 b Fn(g)24
b Fo(is)h(simply)g(c)l(onne)l(cte)l(d,)g(extends)722
2989 y(to)30 b(in\014nity,)g(and)g(satis\014es)1184 3192
y Fr(F)g Fn(\\)19 b(f)o Fr(z)e Fn(j)d Fo(R)l(e)g Fr(z)26
b(>)d(\027)5 b Fn(g)22 b(\032)1935 3099 y Fh(n)1990 3192
y Fr(z)c Fn(j)c Fo(Im)f Fr(z)27 b Fn(2)2341 3099 y Fh(h)2380
3192 y Fr(\030)c Fn(\000)2534 3135 y Fr(c)p 2532 3172
42 4 v 2532 3248 a Fs(2)2583 3192 y Fr(;)14 b(\030)23
b Fs(+)2774 3135 y Fr(c)p 2772 3172 V 2772 3248 a Fs(2)2823
3099 y Fh(io)722 3397 y Fo(for)31 b(some)f Fr(\030)d
Fn(2)d Fm(R)p Fo(.)639 3580 y Fs(With)g(this)g(de\014nition)f(w)n(e)g
(can)f(no)n(w)h(c)n(haracterize)e(parts)h(of)h(the)h(stable)e(set)h(as)
g(sho)n(wn)515 3680 y(in)28 b([6)o(].)515 3846 y Fi(Theorem)33
b(2.1.)41 b Fo(Supp)l(ose)33 b Fr(z)1472 3858 y Fp(0)1509
3846 y Fr(;)14 b(:::;)g(z)1691 3858 y Fq(n)p Fl(\000)p
Fp(1)1852 3846 y Fo(is)32 b(an)g(attr)l(acting)g(p)l(erio)l(dic)i
(orbit)f(for)g Fr(E)3153 3858 y Fq(\025)3228 3846 y Fo(with)515
3945 y Fr(n)28 b Fn(\025)h Fs(2)p Fo(.)48 b(Supp)l(ose)33
b Fs(0)28 b Fn(2)h Fr(A)1337 3915 y Fl(\003)1376 3945
y Fs(\()p Fr(z)1447 3957 y Fp(1)1484 3945 y Fs(\))p Fo(.)49
b(Then)33 b(ther)l(e)g(exist)g(disjoint,)i(op)l(en,)g(simply)f(c)l
(onne)l(cte)l(d)515 4045 y(sets)29 b Fr(C)737 4057 y
Fp(0)775 4045 y Fr(;)14 b(:::;)g(C)977 4057 y Fq(n)p
Fl(\000)p Fp(1)1137 4045 y Fo(such)30 b(that)515 4228
y Fi(i\))41 b Fr(z)659 4240 y Fq(j)717 4228 y Fn(2)23
b Fr(C)854 4240 y Fq(j)889 4228 y Fo(,)30 b Fr(C)1003
4240 y Fq(j)1062 4228 y Fn(\032)22 b Fr(A)1211 4198 y
Fl(\003)1250 4228 y Fs(\()p Fr(z)1321 4240 y Fq(j)1356
4228 y Fs(\))p Fo(.)515 4394 y Fi(ii\))40 b Fr(E)707
4406 y Fq(\025)751 4394 y Fs(\()p Fr(C)842 4406 y Fp(0)880
4394 y Fs(\))23 b(=)g Fr(C)1082 4406 y Fp(1)1138 4394
y Fn(\000)18 b(f)p Fs(0)p Fn(g)p Fo(.)515 4560 y Fi(iii\))40
b Fr(E)734 4572 y Fq(\025)792 4560 y Fs(\()p Fr(C)883
4572 y Fq(j)918 4560 y Fs(\))24 b(=)e Fr(C)1120 4572
y Fq(j)s Fp(+1)1240 4560 y Fo(,)30 b Fr(j)e Fs(=)22 b(1)p
Fr(;)14 b(:::;)g(n)k Fn(\000)g Fs(2)29 b Fo(and)i Fr(E)2074
4572 y Fq(\025)2131 4560 y Fs(\()q Fr(C)2223 4572 y Fq(n)p
Fl(\000)p Fp(1)2353 4560 y Fs(\))23 b Fn(\032)g Fr(C)2555
4572 y Fp(0)2593 4560 y Fo(.)515 4726 y Fi(iv\))41 b
Fr(C)729 4738 y Fp(1)767 4726 y Fr(;)14 b(:::;)g(C)969
4738 y Fq(n)p Fl(\000)p Fp(1)1129 4726 y Fo(ar)l(e)30
b(\014ngers)g(of)g(width)h Fr(c)1895 4738 y Fq(j)1953
4726 y Fn(\024)23 b Fs(2)p Fr(\031)s Fo(.)515 4892 y
Fi(v\))42 b Fo(The)35 b(c)l(omplement)f(of)h Fr(C)1439
4904 y Fp(0)1511 4892 y Fo(c)l(onsists)f(of)g(in\014nitely)h(many)f
(disjoint)h(\014ngers)f(of)h(width)722 4991 y Fs(2)p
Fr(\031)s Fo(.)1926 5255 y Fs(4)p eop
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