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Everything about Feigenbaum function
Concept in dynamical systems
In the study of dynamical systems the term Feigenbaum function has been used to describe two different functions introduced by the physicist Mitchell Feigenbaum:the solution to the Feigenbaum-Cvitanović functional equation; and the scaling function that described the covers of the attractor of the logistic map Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Feigenbaum functionA 5-minute orientation
- Skim a recent paper: Effective algorithms for solving functional equations with superposition on the example of the Feigenbaum equationInfluential work since 2022
- Pick up a classic book: Computer methods and Borel summability applied to Feigenbaum's equationThe most-reprinted book on the subject
- Read the landmark paper: Analyticity properties of the Feigenbaum functionCited 24 times
- Go sideways: Feigenbaum constantsA closely related topic
- Go sideways: Logistic mapA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Analyticity properties of the Feigenbaum function
Fractal boundary of domain of analyticity of the Feigenbaum function and relation to the Mandelbrot set
SYMBOL-TO-SYMBOL CORRELATION FUNCTION AT THE FEIGENBAUM POINT OF THE LOGISTIC MAP
THE EXTENSION OF THE FEIGENBAUM-CVITANOVIĆ FUNCTION TO THE COMPLEX PLANE
The Feigenbaum functional equation and periodic points
🆕 Influential since 2022
📚 Books worth reading
- 📕Computer methods and Borel summability applied to Feigenbaum's equationJean Pierre Eckmann · 1985
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Feigenbaum constants In mathematics, specifically bifurcation theory, the Feigenbaum constants /ˈfaɪɡənbaʊm/ δ and α are two mathematical constants which both express ratios…
- Logistic map The logistic map is a discrete dynamical system defined by the quadratic difference equation It is a recurrence relation and a polynomial mapping of degree 2…
- Oscar Lanford Oscar Erasmus Lanford III (January 6, 1940 – November 16, 2013) was an American mathematician working on mathematical physics and dynamical systems theory…
- Mitchell Feigenbaum Mitchell Jay Feigenbaum /ˈfaɪɡənˌbaʊm/ (December 19, 1944 – June 30, 2019) was an American mathematical physicist whose pioneering studies in chaos theory…
- Bifurcation diagram In mathematics, particularly in dynamical systems, a bifurcation diagram shows the values visited or approached asymptotically (fixed points, periodic…
- Hénon map In mathematics, the Hénon map is a discrete-time dynamical system. It is one of the most studied examples of dynamical systems that exhibit chaotic behavior…
- Period-doubling bifurcation In dynamical systems theory, a period-doubling bifurcation occurs when a slight change in a system's parameters causes a new periodic trajectory to emerge…
- Bifurcation theory Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves…