Quantitative universality for a class of nonlinear transformations

1978/07/01 by Mitchell J. Feigenbaum · 49 citations
Mathematics · Computer Science · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems

paper · doi:10.1007/bf01020332

Cited by

• Discrete-time growth-dispersal models
• The onset of Alfvénic turbulence
• Dynamics of solitons in nearly integrable systems
• Pattern formation outside of equilibrium
• Chaos in biological systems
• Commensurate phases, incommensurate phases and the devil's staircase
• Physics of bubble oscillations
• Quantum logistic map considered as discrete-time Heisenberg equation
• InputDSA: Demixing then Comparing Recurrent and Externally Driven Dynamics
• Spectral properties of the period-doubling operator
• Period-Bubbling Transition to Chaos in Thermo-Viscoelastic Fluid Systems
• Phase Transitions and Order Parameters in Correlation Matrices: A Wishart-Ensemble Perspective on the Largest Eigenvalue
• Approximating Chaotic Attractors by Period-Three Cycles in Discrete Stochastic Systems
• Beyond Lipschitz Continuity and Monotonicity: Fractal and Chaotic Activation Functions in Echo State Networks
• Delay factors in the genesis of limit sets of the non-ideal system "tank with liquid-electric motor"
• Convergence Dynamics and Scaling Laws in the Dissipative Relativistic Kicked Rotator
• Bifurcation Analysis of the Driven FitzHugh-Nagumo Oscillator: Prediction and Experiment
• On-off Threshold Models of Social Contagion
• Parameter Estimation in Models with Complex Dynamics
• Discrete-time travelling waves: Ecological examples
• Rigorous computer-assisted bounds on renormalisation fixed point functions, eigenfunctions, and universal constants
• Implementation of a generalized intermittency scenario in the Rossler dynamical system
• On Helmholtz free energy for finite abstract simplicial complexes
• On the optimal allocation of assets in investment portfolio with\n application of modern portfolio and nonlinear dynamic chaos theories in\n investment, commercial and central banks
• Computational information for the logistic map at the chaos threshold
• Using machine learning to predict statistical properties of non-stationary dynamical processes: System climate,regime transitions, and the effect of stochasticity
• Regularity properties of critical invariant circles of twist maps, and their universality
• Fractal Analysis for Social Systems
• Notation for Iteration of Functions, Iteral
• Nonlinear dynamics in breathing-soliton lasers
• Rigorous bounds on the Hausdorff dimension of Feigenbaum attractors
• Sensitivity dependence of the Navier-Stokes turbulence of a two-dimensional Rayleigh-Bénard convection on time-step
• On the Dynamics of Complex Quadratic Families under Holomorphic and Non-Holomorphic Singular Perturbations
• Quantum Signatures of Strange Attractors
• The discontinuous dynamics and non-autonomous chaos
• Chaotic interaction between thermodynamic systems
• Deep Learning for Analyzing Chaotic Dynamics in Biological Time Series: Insights from Frog Heart Signals
• Observation of period doubling and chaos in spin-wave instabilities in yttrium iron garnet
• Forecasting Low-Dimensional Turbulence via Multi-Dimensional Hybrid Quantum Reservoir Computing
• The boundary of chaos for piecewise smooth maps and the boundary of positive Hausdorff dimension for survivor sets of open maps
• Econophysics deserves a revamping
• Can renormalization group flow end in a Big Mess?
• Symbol-to-symbol correlation function at the Feigenbaum point of the logistic map
• An efficient method for the computation of the Feigenbaum constants to high precision
• Topological conjugation of one dimensional maps
• Universality in the Distribution of Caustics in the Expanding Universe
• Dynamical Systems Applied to Asymptotic Geometry
• Chaos in neural networks with a nonmonotonic transfer function
• Logistic map [wikipedia]