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Bull. of r e s t r i c t i o n s of the Global Bull. I. Math. fixed point zeta f u n c t i o n . , minimum Sci. theory. , 1968, 1941, 1940, of the 43-49. 117, - Contemporary 45-55. 659-671. , 1983, 1-108. V. 1982, 14. 265, 284-286. P. 14, Symp. , 1970, surface. 18. - theory Math. topologique. Acad. Systems. 14, Global Analysis, Proc. 23-41. and dynamics of d i f f e o m o r p h i s m s 1977. , Proc. , -Sov. 109-132. P. et e n t r o p i c D. H o m o l o g y R. T o p o l o g i c a l 17. T h u r s t o n numbers.

PROBLEM. For which spaces and maps Nielsen zeta function N{(~)is a rational function or a radical from a rational function ? Is N~(~ an algebraic function ? When N~(~) is rational or a radical from rational function the infinite sequence of the Nielsen numbers { N { I ~ )}~=~ by a finite set of complex numbers - zeroes and poles of Lemma I ). e. =~, p,, p~. 0 , If I is a periodic Ntlz) = if p2, I C~ for some prime map of least period ~I. ,l~ d, lm, The Nielsen zeta function T is rational automorphisms of for e x p a n d i n g maps of the orientable ~ , for hyperbolic nuous maps of the projective LEMMA I.

The N i e l s e n zeta function. anal. 19, N 4, 61-67. Funk. , I1azur B. On p e r i o d i c points. 81, N I, 82-99. 4 5 6 Smale S. 73, Franks 7 1982, N 49, Fried D. Periodic Amer. 8 9 10 Math. , Shift transformation. - Proc. G. D ~ t e r m i n a t i o n 1971, F. - Bull. of r e s t r i c t i o n s of the Global Bull. I. Math. fixed point zeta f u n c t i o n . , minimum Sci. theory. , 1968, 1941, 1940, of the 43-49. 117, - Contemporary 45-55. 659-671. , 1983, 1-108. V. 1982, 14. 265, 284-286. P.

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