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A note on a generalization of Diliberto's Theorem for certain differential equations of higher dimension

Ladislav Adamec (2005)

Applications of Mathematics

In the theory of autonomous perturbations of periodic solutions of ordinary differential equations the method of the Poincaré mapping has been widely used. For the analysis of properties of this mapping in the case of two-dimensional systems, a result first obtained probably by Diliberto in 1950 is sometimes used. In the paper, this result is (partially) extended to a certain class of autonomous ordinary differential equations of higher dimension.

A note on the structure of quadratic Julia sets

Karsten Keller (1997)

Commentationes Mathematicae Universitatis Carolinae

In a series of papers, Bandt and the author have given a symbolic and topological description of locally connected quadratic Julia sets by use of special closed equivalence relations on the circle called Julia equivalences. These equivalence relations reflect the landing behaviour of external rays in the case of local connectivity, and do not apply completely if a Julia set is connected but fails to be locally connected. However, rational external rays land also in the general case. The present...

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