Basin boundaries and focal points in a map coming from Bairstow’s method

DOI10.1063/1.166414zbMath0982.37033OpenAlexW2026265058WikidataQ52015409 ScholiaQ52015409MaRDI QIDQ4515100

Gian-Italo Bischi, Danièle Fournier-Prunaret, Laura Gardini

Publication date: 12 November 2000

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.166414

zbMATH Keywords

singularitiesbasin of attractionglobal bifurcationsfocal pointsBairstow's methodtwo-dimensional noninvertible mapmaps with a vanishing denominatorprefocal curves

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Low-dimensional dynamical systems (37E99) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (6)

PLANE MAPS WITH DENOMINATOR. PART III: NONSIMPLE FOCAL POINTS AND RELATED BIFURCATIONS ⋮ Real qualitative behavior of a fourth-order family of iterative methods by using the convergence plane ⋮ Path Dependence in Models with Fading Memory or Adaptive Learning ⋮ Plane Maps with Denominator. Part II: Noninvertible Maps with Simple Focal Points ⋮ UNBOUNDED SETS OF ATTRACTION ⋮ KNOT POINTS IN TWO-DIMENSIONAL MAPS AND RELATED PROPERTIES

Cites Work

• On the iteration of a rational function: Computer experiments with Newton's method
• On the concept of attractor
• On the convergence and divergence of Bairstow's method
• Nonconvergence in Bairstow’s Method
• RIDDLED BASINS
• From attractor to chaotic saddle: a tale of transverse instability
• Basin Fractalization Due to Focal Points in a Class of Triangular Maps
• On noninvertible mappings of the plane: Eruptions
• Intermingled basins for the triangle map
• A Generalization of the Bairstow Process

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