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Critical three-cycle dynamics for secant map model

Published on:

14 May 2024

Primary Category:

Dynamical Systems

Paper Authors:

Ernest Fontic,

Antonio Garijo,

Xavier Jarque

Bullets

Key Details

Studies model map capturing secant method's critical three-cycle

Boundary of attraction basin depends on parameter parity and sign

Can be stable manifold of fixed point or two-cycle

Shape includes topological disks or unbounded open sets

Describes chaotic dynamics on boundary in some cases

AI generated summary

Critical three-cycle dynamics for secant map model

This paper analyzes a model map encoding the dynamics of the secant root-finding method near critical periodic points. The model's basin of attraction shape depends on parameter parity and sign. Boundaries may contain stable manifolds of fixed points or two-cycles.

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