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January 1, 2026Kyushu Journal of MathematicsOpen Access

Continuity of the Julia Set of the Hénon Map at a Semi-Parabolic Parameter

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Key Points

This research seeks to explore the continuity of invariant sets of the Hénon map as parameters vary.
Investigated a sequence of parameters (c_n, a_n) converging to (c, a) with a semi-parabolic fixed point.
Analyzed the behavior of invariant sets J, J+, and J in relation to parameter convergence.
Demonstrated that invariant sets converge to H c,a as parameters (c_n, a_n) approach (c, a).
Established that convergence holds particularly when |a| is sufficiently small.

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Implication

Investigates continuity of invariant sets in the Hénon map, suggesting parameter behavior impacts dynamics.

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Cite This Study

YAGI Takumi (2026) studied this question.

synapsesocial.com/papers/6a2cf3b4faef96ed7f0561c9 https://doi.org/10.2206/kyushujm.80.1

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Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1Horn maps of semi-parabolic H\'enon maps2024
2Robustness, convergence, and homoclinic classes in the dynamics of the Hénon mapOriginal Research · 2026
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4Pseudo-monodromy and the Mandelbrot set2024
5More on the Concept of Anti-integrability for H\'enon Maps2025

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