Abstract
For a continuous mapping f : M → M on a topological space M, we will give a series of dichotomies of the space M by using different properties which are satisfied by the cascade {f n} generated by f. Roughly, given a point x ∈ M, if there exists a neighborhood U of x such that {f n} is of a property (P) on U, we write x ∈ F(p)(f). Obviously, F(p)(f) is open. Set J (p)(f) = M - F (P) (f). In many cases, F (P) (f) and J (p) (f) are invariant sets on M. We will discuss these sets for some property (P).
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© 1999 Springer Science+Business Media Dordrecht
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Hu, PC., Yang, CC. (1999). Fatou-Julia type theory. In: Differentiable and Complex Dynamics of Several Variables. Mathematics and Its Applications, vol 483. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9299-4_1
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DOI: https://doi.org/10.1007/978-94-015-9299-4_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5246-9
Online ISBN: 978-94-015-9299-4
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