12/24/2019, 06:26 AM

I asked this question in 1993 in the following manner,

Consider two fixed points of the complex exponential map where and and their Lyapunov multipliers .

Can the forward orbit of traverse a region of space dominated by to the region dominated by ?

My numerical research indicated that the answer can be affirmative. The main problem I faced what the chaotic region between . By adjusting the chaotic region becomes arbitrarily thin and several hundred iterations can map to .

Consider two fixed points of the complex exponential map where and and their Lyapunov multipliers .

Can the forward orbit of traverse a region of space dominated by to the region dominated by ?

My numerical research indicated that the answer can be affirmative. The main problem I faced what the chaotic region between . By adjusting the chaotic region becomes arbitrarily thin and several hundred iterations can map to .