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Displaying similar documents to “Attracting dynamics of exponential maps.”

Trees of visible components in the Mandelbrot set

Virpi Kauko (2000)

Fundamenta Mathematicae

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We discuss the tree structures of the sublimbs of the Mandelbrot set M, using internal addresses of hyperbolic components. We find a counterexample to a conjecture by Eike Lau and Dierk Schleicher concerning topological equivalence between different trees of visible components, and give a new proof to a theorem of theirs concerning the periods of hyperbolic components in various trees.

Hyperbolic components of the complex exponential family

Robert L. Devaney, Nuria Fagella, Xavier Jarque (2002)

Fundamenta Mathematicae

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We describe the structure of the hyperbolic components of the parameter plane of the complex exponential family, as started in [1]. More precisely, we label each component with a parameter plane kneading sequence, and we prove the existence of a hyperbolic component for any given such sequence. We also compare these sequences with the more commonly used dynamical kneading sequences.

Repelling periodic points and landing of rays for post-singularly bounded exponential maps

Anna Miriam Benini, Mikhail Lyubich (2014)

Annales de l’institut Fourier

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We show that repelling periodic points are landing points of periodic rays for exponential maps whose singular value has bounded orbit. For polynomials with connected Julia sets, this is a celebrated theorem by Douady, for which we present a new proof. In both cases we also show that points in hyperbolic sets are accessible by at least one and at most finitely many rays. For exponentials this allows us to conclude that the singular value itself is accessible.

Normal points for generic hyperbolic maps

Mark Pollicott (2009)

Fundamenta Mathematicae

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We consider families of hyperbolic maps and describe conditions for a fixed reference point to have its orbit evenly distributed for maps corresponding to generic parameter values.

C¹-maps having hyperbolic periodic points

N. Aoki, Kazumine Moriyasu, N. Sumi (2001)

Fundamenta Mathematicae

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We show that the C¹-interior of the set of maps satisfying the following conditions: (i) periodic points are hyperbolic, (ii) singular points belonging to the nonwandering set are sinks, coincides with the set of Axiom A maps having the no cycle property.

Poincaré-Hopf index and partial hyperbolicity

C. A Morales (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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We use the theory of partially hyperbolic systems [HPS] in order to find singularities of index 1 for vector fields with isolated zeroes in a 3 -ball. Indeed, we prove that such zeroes exists provided the maximal invariant set in the ball is partially hyperbolic, with volume expanding central subbundle, and the strong stable manifolds of the singularities are unknotted in the ball.

Contractive curves.

Bonifant, Araceli, Dabija, Marius (2002)

International Journal of Mathematics and Mathematical Sciences

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