All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 38 Next

Displaying 741 – 760 of 4754

Showing per page

Chaotic behaviour of the map x ↦ ω(x, f)

Emma D’Aniello, Timothy Steele (2014)

Open Mathematics

Let K(2ℕ) be the class of compact subsets of the Cantor space 2ℕ, furnished with the Hausdorff metric. Let f ∈ C(2ℕ). We study the map ω f: 2ℕ → K(2ℕ) defined as ω f (x) = ω(x, f), the ω-limit set of x under f. Unlike the case of n-dimensional manifolds, n ≥ 1, we show that ω f is continuous for the generic self-map f of the Cantor space, even though the set of functions for which ω f is everywhere discontinuous on a subsystem is dense in C(2ℕ). The relationships between the continuity of ω f and...

Characteristic Exponents of Rational Functions

Anna Zdunik (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

We consider two characteristic exponents of a rational function f:ℂ̂ → ℂ̂ of degree d ≥ 2. The exponent χ a ( f ) is the average of log∥f’∥ with respect to the measure of maximal entropy. The exponent χ m ( f ) can be defined as the maximal characteristic exponent over all periodic orbits of f. We prove that χ a ( f ) = χ m ( f ) if and only if f(z) is conformally conjugate to z ↦ z ± d .

Characterization of ω -limit sets of continuous maps of the circle

David Pokluda (2002)

Commentationes Mathematicae Universitatis Carolinae

In this paper we extend results of Blokh, Bruckner, Humke and Sm’ıtal [Trans. Amer. Math. Soc. 348 (1996), 1357–1372] about characterization of ω -limit sets from the class 𝒞 ( I , I ) of continuous maps of the interval to the class 𝒞 ( 𝕊 , 𝕊 ) of continuous maps of the circle. Among others we give geometric characterization of ω -limit sets and then we prove that the family of ω -limit sets is closed with respect to the Hausdorff metric.

Chordal cubic systems.

Marc Carbonell, Jaume Llibre (1989)

Publicacions Matemàtiques

We classify the phase portraits of the cubic systems in the plane such that they do not have finite critical points, and the critical points on the equator of the Poincaré sphere are isolated and have linear part non-identically zero.

Currently displaying 741 – 760 of 4754