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Universal behavior in nonlinear systems
Abstract A semipopular account of the universal scaling theory for the period doubling route to chaos is presented.
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The universal metric properties of nonlinear transformations
AbstractThe role of functional equations to describe the exact local structure of highly bifurcated attractors ofxn+1 =λf(xn) independent of a specificf is formally developed. A hierarchy ofExpand
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Some characterizations of strange sets
A thermodynamic formalism is exhibited that is the canonical version of Halseyet al.'s microcanonical formulation. This formalism is applied to a four-scale Cantor set and it is shown that theExpand
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The transition to aperiodic behavior in turbulent systems
Some systems achieve aperiodic temporal behavior through the production of successive half subharmonics. A recursive method is presented here that allows the explicit computation of this aperiodicExpand
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Universal behaviour in families of area-preserving maps
We have investigated numerically the behaviour, as a perturbation parameter is varied, of periodic orbits of some reversible area-preserving maps of the plane. Typically, an initially stable periodicExpand
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An interview with Stan Ulam and Mark Kac
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Oxford Hammond atlas of the world
Created entirely from a computer database, this full-size atlas researches, verifies and digitizes the longitude and latitude of every town, river, border and feature of the Earth's terrain. ItExpand
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The Theory of Relativity - Galileo's Child
We determine the Lorentz transformations and the kinematic content and dynamical framework of special relativity as purely an extension of Galileo's thoughts. No reference to light is ever required:Expand
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Periodic Orbit Expansions for Power Spectra of Chaotic Systems
3 Periodic orbit formulas for evaluation of power spectra of chaotic dynamical systems are derived and tested numerically on several 1dimensional mappings.