# Homoclinic orbit in the Logistic Map

1. Feb 18, 2008

### standardflop

My question is the following: " For the logistic map $x_{k+1} = rx_k(1-x_k)$ the band-merging point, where the period-1 orbit undergoes its first homoclinic bifurcation, is at r=3.678573510. Draw a trajectory to the map that illustrates the homoclinic orbit. "

The period-1 orbit is at the diagonals intersection with the parabola, correct?
I know what a homoclinic orbit looks like in a time-continuous system - it goes away from a fixed point, back to the same fixed point.. but what does it look like in a iterated map (the logistic map)?

Regards.

Last edited: Feb 18, 2008