Cubic polynomials with a parabolic point
Pascale Roesch
TL;DR
This paper studies cubic polynomials with a parabolic fixed point, proving that the boundary of the immediate basin of attraction is a Jordan curve and describing the dynamics involved.
Contribution
It provides a rigorous proof that the boundary of the immediate basin is a Jordan curve and offers a detailed description of the polynomial dynamics.
Findings
Boundary of the immediate basin is a Jordan curve
Provides a description of the dynamics near the parabolic point
Establishes structural properties of cubic polynomials with parabolic fixed points
Abstract
We consider the family of cubic polynomials with a simple parabolic fixed point. We prove that the boundary of the immediate basin of attraction of the parabolic point is a Jordan curve and give a description of the dynamics.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Functional Equations Stability Results · advanced mathematical theories