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This research aims to explore the properties of a family of linear recurrent sequences with a specific negative coefficient.

March 22, 2026Open Access

A Family of Recurrent Sequences with Oscillatory Stabilization and the √ 2 Limit

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Findings reveal characteristic polynomials of recurrent sequences converge to √2, suggesting unique stability properties.

This research aims to explore the properties of a family of linear recurrent sequences with a specific negative coefficient.
Theoretical analysis of the characteristic polynomials of linear recurrent sequences.
High-precision numerical calculations to support the theoretical findings.
Demonstrated that the moduli of dominant roots of the sequences converge to √2 as the order increases.
Contrasted the limit behavior with classical systems like Pisot numbers, where the limit is 2.

Emma Helmdach (2026) studied this question.

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March 22, 2026Open Access

View Full Paper

Ask AI

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Authors

Findings reveal characteristic polynomials of recurrent sequences converge to √2, suggesting unique stability properties.

This research aims to explore the properties of a family of linear recurrent sequences with a specific negative coefficient.
Theoretical analysis of the characteristic polynomials of linear recurrent sequences.
High-precision numerical calculations to support the theoretical findings.
Demonstrated that the moduli of dominant roots of the sequences converge to √2 as the order increases.
Contrasted the limit behavior with classical systems like Pisot numbers, where the limit is 2.

Emma Helmdach (2026) studied this question.

View Full Paper

Ask AI

Bookmark