Classical Dynamics of Particles and Systems · Problem 4-17

Gravitation — Marion & Thornton

Physics — Mechanics · tent-map

Problem

The tent map is represented by the following iterations: xn+1=2αxnfor 0<x<1/2x_{n+1} = 2\alpha x_n \qquad \text{for } 0 < x < 1/2 xn+1=2α(1−xn)for 1/2<x<1x_{n+1} = 2\alpha(1 - x_n) \quad \text{for } 1/2 < x < 1 where 0<α<10 < \alpha < 1. Make a map up to 20 iterations for α=0.4\alpha = 0.4 and 0.7 with x1=0.2x_1 = 0.2. Does it appear that either of the maps represent chaotic behavior?

Browse the problem library