主講者: | 王季豪先生 (中央大學) |
講題: | On generalized (m,n)-dynatomic polynomials |
時間: | 2011-12-13 (Tue.) 14:30 - 15:45 |
地點: | 數學所 617 研討室 (台大院區) |
Abstract: | In the classical case, the n-th cyclotomic polynomial is defined by $\prod_{d|n}(x^d-1)^mu(n/d)$ which is the polynomial whose roots are the primitive n-th roots of unity. Let $f$ be a rational map. We also want to study its n-th dynatomic "polynomial": $\prod_{d|n}(f^d(x)-x)^mu(n/d)$. Is this really a polynomial? It is also interesting to study the roots of this "polynomial" . For example, are they exact n-th periodic points? We also want to discuss a more general question:how to define the generalized (m,n)-dynatomic "polynomial" for the preperiodic point with "tail" of length m and period n? |
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