On weak orbits of operators
✍ Scribed by C. Badea; V. Müller
- Book ID
- 108286536
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 146 KB
- Volume
- 156
- Category
- Article
- ISSN
- 0166-8641
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We prove that if the multipliers of the repelling periodic orbits of a complex polynomial grow at least like n 5+ε with the period, for some ε > 0, then the Julia set of the polynomial is locally connected when it is connected. As a consequence for a polynomial the presence of a Cremer cycle implies
## Abstract A bounded linear operator __T__ on a Banach space __X__ is called hypercyclic if there exists a vector __x__ ∈ __X__ such that its orbit, {__T^n^x__ }, is dense in __X__. In this paper we show hypercyclic properties of the orbits of the Cesàro operator defined on different spaces. For i