Displaying similar documents to “Dynamics of certain nonconformal degree-two maps of the plane.”

A dynamical invariant for Sierpiński cardioid Julia sets

Paul Blanchard, Daniel Cuzzocreo, Robert L. Devaney, Elizabeth Fitzgibbon, Stefano Silvestri (2014)

Fundamenta Mathematicae


For the family of rational maps zⁿ + λ/zⁿ where n ≥ 3, it is known that there are infinitely many small copies of the Mandelbrot set that are buried in the parameter plane, i.e., they do not extend to the outer boundary of this set. For parameters lying in the main cardioids of these Mandelbrot sets, the corresponding Julia sets are always Sierpiński curves, and so they are all homeomorphic to one another. However, it is known that only those cardioids that are symmetrically located...

Intertwined internal rays in Julia sets of rational maps

Robert L. Devaney (2009)

Fundamenta Mathematicae


We show how the well-known concept of external rays in polynomial dynamics may be extended throughout the Julia set of certain rational maps. These new types of rays, which we call internal rays, meet the Julia set in a Cantor set of points, and each of these rays crosses infinitely many other internal rays at many points. We then use this construction to show that there are infinitely many disjoint copies of the Mandelbrot set in the parameter planes for these maps.

Turbulent maps and their ω-limit sets

F. Balibrea, C. La Paz (1997)

Annales Polonici Mathematici


One-dimensional turbulent maps can be characterized via their ω-limit sets [1]. We give a direct proof of this characterization and get stronger results, which allows us to obtain some other results on ω-limit sets, which previously were difficult to prove.

Symbolic dynamics and Lyapunov exponents for Lozi maps

Diogo Baptista, Ricardo Severino (2012)

ESAIM: Proceedings


Building on the kneading theory for Lozi maps introduced by Yutaka Ishii, in 1997, we introduce a symbolic method to compute its largest Lyapunov exponent. We use this method to study the behavior of the largest Lyapunov exponent for the set of points whose forward and backward orbits remain bounded, and find the maximum value that the largest Lyapunov exponent can assume.

The dynamics of two-circle and three-circle inversion

Daniel M. Look (2008)

Fundamenta Mathematicae


We study the dynamics of a map generated via geometric circle inversion. In particular, we define multiple circle inversion and investigate the dynamics of such maps and their corresponding Julia sets.

Simple and complex dynamics for circle maps.

Lluís Alsedà, Vladimir Fedorenko (1993)

Publicacions Matemàtiques


The continuous self maps of a closed interval of the real line with zero topological entropy can be characterized in terms of the dynamics of the map on its chain recurrent set. In this paper we extend this characterization to continuous self maps of the circle. We show that, for these maps, the chain recurrent set can exhibit a new dynamic behaviour which is specific of the circle maps of degree one.