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Green-function and information–geometric correspondences between inverse eigenvalue loci of generalized Lucas sequences and the Mandelbrot set

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  • Ortiz–Tapia, Arturo

Abstract

We investigate geometric, potential-theoretic, and information-theoretic correspondences between the inverse eigenvalue loci of companion matrices associated with generalized Lucas sequences and the boundary of the Mandelbrot set. Through systematic numerical experiments, we show that these algebraic spectral loci exhibit a striking low-distortion geometric correspondence with the Mandelbrot boundary at macroscopic scales, together with a coherent organization within its external potential field, characterized by concentration along narrow equipotential annuli of the Mandelbrot Green function.

Suggested Citation

  • Ortiz–Tapia, Arturo, 2026. "Green-function and information–geometric correspondences between inverse eigenvalue loci of generalized Lucas sequences and the Mandelbrot set," Chaos, Solitons & Fractals, Elsevier, vol. 208(P2).
    • Handle: RePEc:eee:chsofr:v:208:y:2026:i:p2:s0960077926003322
    DOI: 10.1016/j.chaos.2026.118191
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