Bifurcation rigidity

DOI10.1016/S0167-2789(98)00201-2zbMath0951.37010OpenAlexW2913119130MaRDI QIDQ1808267

Jason A. C. Gallas, Celso Grebogi, James A. Yorke, Brian R. Hunt, Hueseyin Kocak

Publication date: 6 December 1999

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(98)00201-2

zbMATH Keywords

critical pointbifurcation diagramsinterval maps

Mathematics Subject Classification ID

Symbolic dynamics (37B10) Dynamical systems involving maps of the interval (37E05)

Related Items (10)

CHAOS INDUCEMENT AND ENHANCEMENT IN TWO PARTICULAR NONLINEAR MAPS USING WEAK PERIODIC/QUASIPERIODIC PERTURBATIONS ⋮ CHARACTERIZATION OF THE RÖSSLER SYSTEM IN PARAMETER SPACE ⋮ Compound windows of the Hénon-map ⋮ The phase-modulated logistic map ⋮ THE STRUCTURE OF INFINITE PERIODIC AND CHAOTIC HUB CASCADES IN PHASE DIAGRAMS OF SIMPLE AUTONOMOUS FLOWS ⋮ Intermittency cascade ⋮ Fractal and riddled basins: arithmetic signatures in the parameter space of two coupled quadratic maps ⋮ Reductions and simplifications of orbital sums in a Hamiltonian repeller ⋮ Multiparameter critical situations, universality and scaling in two-dimensional period-doubling maps ⋮ Conjugation of cascades

Cites Work

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• The universal metric properties of nonlinear transformations
• Scaling of Mandelbrot sets generated by critical point preperiodicity
• How often do simple dynamical processes have infinitely many coexisting sinks?
• Wild hyperbolic sets, yet no chance for the coexistence of infinitely many KLUS-simple Newhouse attracting sets
• Scaling symmetries in nonlinear dynamics. A view from parameter space
• Quantitative universality for a class of nonlinear transformations
• A computer-assisted proof of the Feigenbaum conjectures
• TWO-PARAMETER STUDY OF TRANSITION TO CHAOS IN CHUA'S CIRCUIT: RENORMALIZATION GROUP, UNIVERSALITY AND SCALING
• THE ROLE OF CODIMENSION IN DYNAMICAL SYSTEMS

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