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(2) Consider any initial condition (x0,y0) for the cat map. Show that there exist infinitely many points (x,y) so that the distance between ƒk (x, y) and fk (x0, y0) converges to 0 as k→∞. Show that nevertheless there is sensitive dependence on initial conditions.

(2) Consider any initial condition (x0,y0) for the cat map. Show that there exist infinitely many points (x,y) so that the distance between ƒk (x, y) and fk (x0, y0) converges to 0 as k→∞. Show that nevertheless there is sensitive dependence on initial conditions.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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(2) Consider any initial condition (x0,y0) for the cat map. Show that there exist infinitely many points (x.y) so that the distance between fk (x, y) and fk (x0, y0) converges to 0 as k → 00. Show that nevertheless there is sensitive dependence on initial conditions.
Transcribed Image Text:(2) Consider any initial condition (x0,y0) for the cat map. Show that there exist infinitely many points (x.y) so that the distance between fk (x, y) and fk (x0, y0) converges to 0 as k → 00. Show that nevertheless there is sensitive dependence on initial conditions.
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