Chapter 10.5, Problem 3E

Interpretation Introduction

Interpretation:

To analyse the dynamics of the tent map for $\text{r}\le \text{1}$.

Concept Introduction:

• ➢ Logistic map can exhibit aperiodic orbits for certain parameter values.

• ➢ Tent map is piecewise linear so that the tent map is far easier to analyze than the logistic map.

• ➢ Apositive Liapunov exponent is a signature of chaos.

• ➢ For $\text{λ = lnr}$ the tent map, independent of the initial condition ${\text{x}}_{\text{0}}$.