Operating with external arguments of Douady and Hubbard.

Pastor, G.; Romera, M.; Alvarez, G.; Nunez, J.; Arroyo, D.; Montoya, F.

Displaying similar documents to “Operating with external arguments of Douady and Hubbard.”

Trees of visible components in the Mandelbrot set

Virpi Kauko (2000)

Fundamenta Mathematicae

Similarity:

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.

Coupling patterns of external arguments in the multiple-spiral medallions of the Mandelbrot set.

Romera, M., Pastor, G., Orue, A.B., Arroyo, D., Montoya, F. (2009)

Discrete Dynamics in Nature and Society

Similarity:

Attracting dynamics of exponential maps.

Schleicher, Dierk (2003)

Annales Academiae Scientiarum Fennicae. Mathematica

Similarity:

Devil's staircase route to chaos in a forced relaxation oscillator

Lluis Alsedà, Antonio Falcó (1994)

Annales de l'institut Fourier

Similarity:

We use one-dimensional techniques to characterize the Devil’s staircase route to chaos in a relaxation oscillator of the van der Pol type with periodic forcing term. In particular, by using symbolic dynamics, we give the behaviour for certain range of parameter values of a Cantor set of solutions having a certain rotation set associated to a rational number. Finally, we explain the phenomena observed experimentally in the system by Kennedy, Krieg and Chua (in [10]) related with the appearance...