On noninvertible mappings of the plane: Eruptions

DOI10.1063/1.166158zbMath1055.37567OpenAlexW2168581605WikidataQ52303403 ScholiaQ52303403MaRDI QIDQ4526362

James H. Curry, Lora Billings

Publication date: 16 January 2001

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

Full work available at URL: https://doi.org/10.1063/1.166158

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Low-dimensional dynamical systems (37E99)

Related Items (11)

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 ⋮ PLANE MAPS WITH DENOMINATOR I: SOME GENERIC PROPERTIES ⋮ Symmetric functions and exact Lyapunov exponents ⋮ UNBOUNDED SETS OF ATTRACTION ⋮ KNOT POINTS IN TWO-DIMENSIONAL MAPS AND RELATED PROPERTIES ⋮ On some properties of focal points ⋮ A route to computational chaos revisited: Noninvertibility and the breakup of an invariant circle ⋮ Basin boundaries and focal points in a map coming from Bairstow’s method

Cites Work

• Computational chaos - a prelude to computational instability
• On the concept of attractor
• Invariant measures for Markov maps of the interval
• Noninvertibility and the structure of basins of attraction in a model adaptive control system
• On the convergence and divergence of Bairstow's method
• Bubbling of attractors and synchronisation of chaotic oscillators
• Nonconvergence in Bairstow’s Method
• BASIN BIFURCATIONS OF TWO-DIMENSIONAL NONINVERTIBLE MAPS: FRACTALIZATION OF BASINS
• A DOUBLE LOGISTIC MAP
• A Nonconverging Newton Sequence
• A Generalization of the Bairstow Process

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