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The cyclic spectrum of a Boolean flow

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John F. Kennison

This paper defines flows (or discrete dynamical systems) and cyclic flows
in a category and investigates how the trajectories of a point might
approach a cycle. The paper considers cyclic flows in the categories of
Sets and of Boolean algebras and their duals and characterizes the Stone
representation of a cyclic flow in Boolean algebras. A cyclic spectrum is
constructed for Boolean flows. Examples include attractive fixpoints,
repulsive fixpoints, strange attractors and the logistic equation.

Keywords: flow, discrete dynamical system, topos, Cole spectrum, strange attractor.

2000 MSC: 18B25, 37B99.

*Theory and Applications of Categories*, Vol. 10, 2002, No. 15, pp 392-409.

http://www.tac.mta.ca/tac/volumes/10/15/10-15.dvi

http://www.tac.mta.ca/tac/volumes/10/15/10-15.ps

http://www.tac.mta.ca/tac/volumes/10/15/10-15.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/10/15/10-15.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/10/15/10-15.ps

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