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April 3, 2026Open Access

The Jacobsthal files : Volume I; A Study in Eigenvalues

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Authors

DCDavid Coates

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Overview

Investigations reveal unique eigenvalue relationships in dynamic systems, indicating mathematical boundaries for black holes.

Key Points

  • The aim is to establish unique eigenvalue behaviors in the Jacobsthal sequence and their implications in dynamic systems.
  • Analyzed the recurrence relation x_n = x_{n-1} + c·x_{n-2] with c as a variable coefficient.
  • Derived the dominant eigenvalue and its relation to the coefficient c, focusing on c = 2.
  • Investigated the placement of the Jacobsthal sequence at the parabolic boundary of SL(2,ℝ).
  • Found that c = 2 is the only coefficient where the dominant eigenvalue matches c itself.
  • Demonstrated the Jacobsthal sequence maintains unique characteristics at the parabolic boundary, influencing the dynamics between bounded and chaotic.
  • Confirmed the relationship between rotating black holes and the same boundary, independent of the spin parameter.

Cite This Study

David Coates (2026) studied this question.

synapsesocial.com/papers/69cf5ced5a333a821460a83ehttps://doi.org/10.5281/zenodo.19362565
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