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Introduction to surreal numbers
3rd workshop on nonlinear evolution equations
INTRODUCTION
233
TO SURREAL NUMBERS
M. D. Kruskal, Mathematics Department,
Princeton University
Princeton,,NJ
08544, USA
John H. Conway has introduced a remarkably simple and strikingly extensive number system, which includes the real numbers, a vast class of infinitesimals, and all sorts of infinite numbers including the ordinals. All reasonable familiar arithmetic and analytic operations can be performed on these numbers and functions of them, and they have new structures and properties. A number is most simply constructed as a well ordered sequence (with arbitrary ordinal length) of binary choices, say "up" ( ) and "down" ( )
LOW DIMENSIONAL OCEAN
CHAOTIC BEHAVIOUR
A. Provenzale, Istituto di Fisica Generale,
IN A GEOPHYSICAL SCALE FLOW IN THE PACIFIC
Universita
di Torino,
Torino,
Italy
We discuss the phase space analysis of a time series obtained by satellite tracking the trajectories of three drifters (buoys) deployed in the Kuroshio current in Pacific Ocean. The time series consists of the Lagrangian measurements of the positions of the drifters during a one year period. The data are studied following the method of the phase space correlation function proposed by Grassberger and Procaccia. The results of the analysis suggest that the temporal behaviour of this flow is dominated by a strange (chaotic) attractor of fractal dimension 1.5 and finite Kolmogorov entropy. This is the first evidence of low dimensional, deterministic chaotic dynamics in a natural fluid flow outside the laboratory. This work has been done with A. R. Osborne, A. D. Kirwan and L. Bergamasco.
INTERNAL WAVES IN MARINE STRAITS V. Artale and D. Levi*, ENEA, C.R.E. Ambiente, La Spezia, Italy *Dipartimento di Fisica, Universita di Roma I, Rome,
Italy
By applying a perturbation technique to the Euler equation for a twolayer fluid it can be shown that the evolution of the interface is described by a Korteweg-de Vries equation. This model is used to describe the Tidegeneration of solitons in the strait of Gilbraltar.
INTRODUCTION
233
TO SURREAL NUMBERS
M. D. Kruskal, Mathematics Department,
Princeton University
Princeton,,NJ
08544, USA
John H. Conway has introduced a remarkably simple and strikingly extensive number system, which includes the real numbers, a vast class of infinitesimals, and all sorts of infinite numbers including the ordinals. All reasonable familiar arithmetic and analytic operations can be performed on these numbers and functions of them, and they have new structures and properties. A number is most simply constructed as a well ordered sequence (with arbitrary ordinal length) of binary choices, say "up" ( ) and "down" ( )
LOW DIMENSIONAL OCEAN
CHAOTIC BEHAVIOUR
A. Provenzale, Istituto di Fisica Generale,
IN A GEOPHYSICAL SCALE FLOW IN THE PACIFIC
Universita
di Torino,
Torino,
Italy
We discuss the phase space analysis of a time series obtained by satellite tracking the trajectories of three drifters (buoys) deployed in the Kuroshio current in Pacific Ocean. The time series consists of the Lagrangian measurements of the positions of the drifters during a one year period. The data are studied following the method of the phase space correlation function proposed by Grassberger and Procaccia. The results of the analysis suggest that the temporal behaviour of this flow is dominated by a strange (chaotic) attractor of fractal dimension 1.5 and finite Kolmogorov entropy. This is the first evidence of low dimensional, deterministic chaotic dynamics in a natural fluid flow outside the laboratory. This work has been done with A. R. Osborne, A. D. Kirwan and L. Bergamasco.
INTERNAL WAVES IN MARINE STRAITS V. Artale and D. Levi*, ENEA, C.R.E. Ambiente, La Spezia, Italy *Dipartimento di Fisica, Universita di Roma I, Rome,
Italy
By applying a perturbation technique to the Euler equation for a twolayer fluid it can be shown that the evolution of the interface is described by a Korteweg-de Vries equation. This model is used to describe the Tidegeneration of solitons in the strait of Gilbraltar.