Rigorous Numerical Study of Low-Period Windows for the Quadratic Map

DOI10.1142/S0218127415501394zbMath1326.65174OpenAlexW2200168887MaRDI QIDQ3453711

Zbigniew Galias

Publication date: 30 November 2015

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127415501394

zbMATH Keywords

interval arithmeticlogistic mapperiodic windowquadratic mapinterval Newton operator

Mathematics Subject Classification ID

Dynamical systems involving maps of the interval (37E05) Numerical bifurcation problems (65P30)

Related Items (5)

On examples of pseudohyperbolic attractors in flows and maps ⋮ Scaling and fine structure of superstable periodic orbits in the logistic map ⋮ Limit cycles and their period detection via numeric and symbolic hybrid computations ⋮ Systematic search for wide periodic windows and bounds for the set of regular parameters for the quadratic map ⋮ Interval computing periodic orbits of maps using a piecewise approach

Cites Work

• A rigorous lower bound for the stability regions of the quadratic map
• Almost every real quadratic map is either regular or stochastic.
• Proving the existence of long periodic orbits in 1D maps using interval Newton method and backward shooting
• Quantitative hyperbolicity estimates in one-dimensional dynamics
• Interval Methods for Systems of Equations
• On the structure of existence regions for sinks of the Hénon map
• Simple mathematical models with very complicated dynamics

This page was built for publication: Rigorous Numerical Study of Low-Period Windows for the Quadratic Map