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# Abstract. Let f be a continuous map of the circle S

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(1)

157 (1998)

1

1

(h−ε)nk

k

nk

0

(h−ε)nk

k

hn

n→∞

n

n

n

1

1

1

[245]

(2)

n

ni

n

0

ni

n

1

1

k

k=0

k

(h−ε)nk

nik

k

nk

0

nik

(h−ε)nk

1

1+ε

1+ε

1

1

1+ε

1+ε

1

(3)

1

1

l

l

nl

nil

[ai=1nl]

1

1

m

nil

l

nil

nil

nil

l

nil

nl−1

m=0

[anl]

i=1

m

nil

nl

nl

nil

l

nl

i

l

nl

0

i

nl

nil

inl

nl

nl

0

inl

nl

nil

l

nil

inl

nl

0

inl

nl

0

nil

εnl

nil

g

g

(4)

1

+

f,ψ

n

i=1

f0

i

n i=1

i

i

0

δ→0

f0

f0

n

i=1

i

i

n i=1

f0

i

i:δi

i:δi≥γ

f0

l

nl

nil

Ai=1

A

i=1

nil

nl

−nl

nl

nil

nl

inl

nil

nl

0

inl

−nl

nl

A

i=1

nl−1

k=0

k

nil

nl

n

l−1 k=0

k

nil

l

nl

l

nl

l

nl

nil

nil

n

l−1 k=0

k

nil

l

nil

i

l

nl

0

k

nil

nl

0

k

nil

nl

0

nil

nl

0

nil

k∈Si

0

k

nil

0

k

nil

−1

k∈Si

0

k

inl

0

k

nil

(5)

−1

n

l−1 k=0

0

k

inl

0

k

nil

−1

n

l−1 k=0

f0

k

nil

l

0

n−1

k=0

f0

k

nil

l

l

nl

0

inl

nl

0

nil

l

nl

0

nil

nl

0

nil

εnl

nl

εnl

ε

nl

l

nil

l

nl

nil

inl

nl

0

inl

nl

nl

nil

l

nl

0

nil

nl

1

1

1

n

ni

ki=1n

n

1

0

(6)

n

ni

1

m

ni

ki=1n

m

kn

i=1

m

ni

m

n−1

m=0 kn

i=1

m

ni

n

n

ni

n

0

ni

n

1

1

0

AR

AR

¹ΩR

A

¹ΩR

A

AR

AR

AR

(i)

1i

i2

in

AR

AR

RA

1i

i2

ir

(i)

¹F

R

A

1

2

n

s

(i)

1i

i2

ir

s

s+1

s+2

s+r

(7)

s+1

i1

s+r

ir

1i

2i

ri

¹F

k

k=1

(h(σ|F)−ε)nk

(h−3ε)nk

k

(ni k)

k

h−3ε

12

(h−3ε)nk

nik

k

0

nik

(h−4ε)nk

1

1

1

χ

n

ni

n

0

ni

n

12

0

−1

n−1

k=0

k

−1

n

0

n

0

12

n

ni

n

0

12

n

ni

n

12

12

(8)

1

1

n

0

ni

n

n

0

ni

n

n

0

ni

n

1

1

1

χ

0

1+ε

k

n

n

1

n

1

1

1

¹Λ

¹V

(9)

n→∞

n

µ

µ

¹J

r

## diffeomorphisms of compact two-dimensional manifolds [KT] and also geodesic flows on rank one manifolds of non-positive curva- ture [Kn].

(10)

1

1+α

1

### in revised form 2 March 1998

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