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Quantitative universality for a class of nonlinear transformations
AbstractA large class of recursion relationsxn + 1 = λf(xn) exhibiting infinite bifurcation is shown to possess a rich quantitative structure essentially independent of the recursion function. TheExpand
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Quasiperiodicity in dissipative systems: A renormalization group analysis
Abstract Dynamical systems with quasiperiodic behavior, i.e., two incommensurate frequencies, may be studied via discrete maps which show smooth continuous invariant curves with irrational windingExpand
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The onset spectrum of turbulence
Abstract A general theory for the fluctuation spectrum of the onset of turbulence is developed, applying to systems that approach turbulence through a cascade of subharmonic bifurcations. Applied toExpand
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THE METRIC UNIVERSAL PROPERTIES OF PERIOD DOUBLING BIFURCATIONS AND THE SPECTRUM FOR A ROUTE TO TURBULENCE
The ideas of the metric universal properties of maps on an interval are formally developed and then used to determine some universal aspects of a route to turbulence.
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Scaling spectra and return times of dynamical systems
The grand canonical version of the spectrum of singularities formalism is presented, relying naturally upon certain Markov transition graphs. The structure of a graph is simply determined by theExpand
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THE ONSETSPECTRUM OF TURBULENCE
A general theory for the fluctuation spectrum of the onset of turbulence is developed,applying to systemsthat approach turbulence through a cascadeof subharmonic bifurcations. Applied toExpand
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Presentation functions, fixed points, and a theory of scaling function dynamics
Presentation functions provide the time-ordered points of the forward dynamics of a system as successive inverse images. They generally determine objects constructed on trees, regular or otherwise,Expand
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Dynamics of Finger Formation in Laplacian Growth Without Surface Tension
We study the dynamics of “finger” formation in Laplacian growth without surface tension in a channel geometry (the Saffman–Taylor problem). We present a pedagogical derivation of the dynamics of theExpand
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