08/09/2007, 10:04 AM
Hey Andrew,
For the actual division of the forum I decided to keep it simple in the beginning. It can then be extended/restructured if there will be too many threads in one category.
Hopefully all the methods of analytic iteration with fixed points you mention will be sometimes covered/presented on this forum.
Regarding terminlogy however for me it looks as if the people from dynamical systems are a different folk. Probably the terms orbit and flow will not establish in the tetration community. But that is of course up to you all.
Your distinction of hyperpower function, tetrational function and tetration (as I guess chosen similar to the names: power function, exponential function and exponentiation operation) is a good one.
For me personally however the prefix "hyper" (or "super") is somewhat unspecific as it means anything above. You dont know which one above while it is clear that "tetration" is the fourth operation.
For example if you take pentation x ^^^ n with fixed exponent n you would also call it hyperpower function.
My counter proposal would be "tetration exponential", "tetration power" and "tetration operation". Or perhaps even shorter "4-exponential", "4-power" and "4-operation", or "4th exponential", "4th power" and "4th operation". Though this is quite uncommon and will probably not establish, the use of "tetration base" and "tetration exponent" to denote \( b \) and \( x \) respectively in \( {}^x b \) should be quite useful.
Your post is besides a quite sophisticated overview of the topic.
For the actual division of the forum I decided to keep it simple in the beginning. It can then be extended/restructured if there will be too many threads in one category.
Hopefully all the methods of analytic iteration with fixed points you mention will be sometimes covered/presented on this forum.
Regarding terminlogy however for me it looks as if the people from dynamical systems are a different folk. Probably the terms orbit and flow will not establish in the tetration community. But that is of course up to you all.
Your distinction of hyperpower function, tetrational function and tetration (as I guess chosen similar to the names: power function, exponential function and exponentiation operation) is a good one.
For me personally however the prefix "hyper" (or "super") is somewhat unspecific as it means anything above. You dont know which one above while it is clear that "tetration" is the fourth operation.
For example if you take pentation x ^^^ n with fixed exponent n you would also call it hyperpower function.
My counter proposal would be "tetration exponential", "tetration power" and "tetration operation". Or perhaps even shorter "4-exponential", "4-power" and "4-operation", or "4th exponential", "4th power" and "4th operation". Though this is quite uncommon and will probably not establish, the use of "tetration base" and "tetration exponent" to denote \( b \) and \( x \) respectively in \( {}^x b \) should be quite useful.
Your post is besides a quite sophisticated overview of the topic.