Non-standard dynamical systems. Shadows of trajectories and abstracts rivers.
Véronique Gautheron, Emmanuel Isambert (1994)
Collectanea Mathematica
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Véronique Gautheron, Emmanuel Isambert (1994)
Collectanea Mathematica
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Lluis Alsedà, Antonio Falcó (1994)
Annales de l'institut Fourier
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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...
Harold Bell (1978)
Fundamenta Mathematicae
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Paul Blanchard, Daniel Cuzzocreo, Robert L. Devaney, Elizabeth Fitzgibbon, Stefano Silvestri (2014)
Fundamenta Mathematicae
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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...
F. Jones (1970)
Fundamenta Mathematicae
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Shaun Bullett, Andrew Curtis (2012)
Annales de la faculté des sciences de Toulouse Mathématiques
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We investigate an explicit holomorphic correspondence on the Riemann sphere with striking dynamical behaviour: the limit set is a fractal resembling the one-skeleton of a tetrahedron and on each component of the complement of this set the correspondence behaves like a Fuchsian group.
R. Duda (1965)
Fundamenta Mathematicae
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Sam Nadler (1972)
Fundamenta Mathematicae
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A. Lelek (1961)
Fundamenta Mathematicae
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John Cobb (1988)
Fundamenta Mathematicae
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