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%%EndProlog
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TeXDict begin
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a4
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%%Page: 1 1
1 0 bop 515 872 a Fh(Length)41 b(minimizing)k(geo)t(desics)d(of)f(the)h
(Hofer's)e(metric)1535 1112 y Fg(J)m(\023)-46 b(er^)d(ome)32
b(Le)h(Crapp)s(er)1691 1307 y(June)h(6)e(2003)639 1602
y Ff(W)-7 b(e)29 b(will)g(discuss)g(su\016cien)n(t)f(conditions)h(for)f
(a)g(Hamiltonian)g(function)i(to)e(generate)515 1702
y(a)38 b(length)h(minimizing)h(geo)r(desic)e(in)h(the)g(Hamiltonian)g
(di\013eomorphism)g(group)f(of)g(a)515 1802 y(symplectic)27
b(manifold)h(endo)n(w)n(ed)f(with)h(the)g(Hofer's)f(metric.)515
1901 y(W)-7 b(e)35 b(will)g(consider)f(the)i(case)e(of)h(the)g
(standard)f(symplectic)h(space)f(\()p Fe(R)2831 1871
y Fd(2)p Fc(n)2916 1901 y Fb(;!)2991 1913 y Fd(0)3028
1901 y Ff(\))h(and)g(the)515 2001 y(case)27 b(of)h(a)g(closed)g
(symplectic)g(manifold)g(suc)n(h)g(that)g(the)h(class)e(of)i(the)f
(symplectic)g(form)515 2101 y(and)f(the)h(\014rst)f(Chern)h(class)e(b)r
(oth)i(v)-5 b(anish)28 b(on)f(the)h(second)f(homotop)n(y)g(group.)515
2200 y(In)37 b(b)r(oth)h(cases)f(results)g(can)g(b)r(e)h(obtained)f(b)n
(y)g(comparing)f(the)i(Hofer's)f(metric)h(with)515 2300
y(Viterb)r(o's)f(in)g(the)g Fe(R)1197 2270 y Fd(2)p Fc(n)1318
2300 y Ff(case)f(and)h(its)g(generalisation)e(b)n(y)i(Sc)n(h)n(w)n(arz)
e(in)i(the)h(case)e(of)g(a)515 2399 y(closed)27 b(manifold.)515
2499 y(Our)38 b(main)i(result)f(states)g(that)h(a)f(geo)r(desic)f(arc)h
(generated)f(b)n(y)h(a)g(non)g(autonomous)515 2599 y(Hamiltonian)g
(function)i Fb(H)50 b Ff(:)44 b([0)p Fb(;)p Ff(1])26
b Fa(\002)g Fb(M)52 b Fa(!)44 b Fe(R)p Ff(,)i(is)39 b(minimizing)i(pro)
n(vided)e(that)h(the)515 2698 y(Hamiltonian)35 b(v)n(ector)g(\014eld)h
(asso)r(ciated)e(to)i Fb(H)43 b Ff(has)35 b(no)g(degenerate)g(p)r(erio)
r(dic)h(orbit)f(of)515 2798 y(p)r(erio)r(d)25 b(smaller)g(than)g(one.)g
(If)h(that)g(is)f(the)h(case)e(the)i(distances)f(b)r(et)n(w)n(een)g
(the)h(endp)r(oin)n(ts)515 2898 y(of)h(the)h(geo)r(desic)f(arc)g(in)g
(Hofer's)g(and)h(Viterb)r(o's)f(metric)h(coincide.)1926
5255 y(1)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF