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	THE NUMBERS OF PERIODIC ORBITS HIDDEN AT FIXED POINTS OF n-DIMENSIONAL HOLOMORPHIC MAPPINGS (II)
	Zhang, Guang Yuan
	2010-10-12 ; 2010-10-12
关键词	Fixed point index periodic point INDEXES MAPS ITERATIONS Mathematics
中文摘要	Let All be the ball vertical bar x vertical bar < 1 in the complex vector space C-n, let f: Delta(n) -> C-n be a holomorphic mapping and let M be a positive integer. Assume that the origin 0 = (0,...,0) is an isolated fixed point of both f and the M-th iteration f(M) of f. Then the (local) Dold index P-M (f, 0) at the origin is well defined, which can be interpreted to be the number of periodic points of period M of f hidden at the origin: any holomorphic mapping f(1): Delta(n) - C-n sufficiently close to f has exactly P-M (f, 0) distinct periodic points of period M near the origin, provided that all the fixed points of f(1)(m) near the origin are simple. Therefore, the number O-M (f, 0) = P-M (f, 0)/M can be understood to be the number of periodic orbits of period M hidden at the fixed point. According to Shub-Sullivan [18] and Chow-Mallet-Paret-Yorke [2], a necessary condition so that there exists at least one periodic orbit of period M hidden at the fixed point, say, O-M (f, 0) >= 1, iss that the linear part of f at the origin has a periodic point of period M. It, is proved by the author in [21] that the converse holds true. In this paper, we continue to study the number O-M(f, 0). We will give a sufficient condition such that O-M (f, 0) >= 2, in the case that all eigenvalues of Df(0) are primitive m(1)-th,..., m(n)-th roots of unity, respectively, and m(1),..., m(n) are distinct primes with M = m(1)...m(n).
语种	英语 ; 英语
出版者	JULIUSZ SCHAUDER CTR NONLINEAR STUDIES ; TORUN ; UL CHOPINA 12/18, TORUN, 87-100, POLAND
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/81256]
专题	清华大学
推荐引用方式 GB/T 7714	Zhang, Guang Yuan. THE NUMBERS OF PERIODIC ORBITS HIDDEN AT FIXED POINTS OF n-DIMENSIONAL HOLOMORPHIC MAPPINGS (II)[J],2010, 2010.
APA	Zhang, Guang Yuan.(2010).THE NUMBERS OF PERIODIC ORBITS HIDDEN AT FIXED POINTS OF n-DIMENSIONAL HOLOMORPHIC MAPPINGS (II)..
MLA	Zhang, Guang Yuan."THE NUMBERS OF PERIODIC ORBITS HIDDEN AT FIXED POINTS OF n-DIMENSIONAL HOLOMORPHIC MAPPINGS (II)".(2010).

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