Lucas eigenset for U matrices j equal 2 to n and their classification in dynamical points

The GitHub repository containing the code used to generate and classify the eigenvalue data is linked under the "Software" section of this Zenodo entry.

This dataset builds upon the ideas introduced in the preprint "Golden Ratios, Lucas Sequences and the Quadratic Family" (arXiv:1806.06007).

"Lucas eigenset for U matrices with j from 2 to n and their classification into dynamical types" contains the union of the multiplicative inverses of eigenvalues for all matrices from j = 1 up to n = 10, 20, ..., as well as the corresponding eigenpoints classified into the five main dynamical categories: Hyperbolic, Misurewicz, Parabolic, Siegel Disk, and Others — according to the classification of points in the Mandelbrot set.

The methodology and purpose of this dataset are explained in the article "Homotopies and Maps between Eigenvalues of some Generalized Lucas Sequences and the Mandelbrot Set" by Arturo Ortiz-Tapia, which links back to these datasets for reproducibility and further exploration.

Eigenvalues were computed from companion matrices of generalized Lucas sequences and classified via complex dynamical criteria inspired by the structure of the Mandelbrot set.

This dataset was generated using symbolic and numerical computation in the Wolfram Language (Wolfram Cloud).