Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation
#14
Not very rigorous argument:

The region around -2 is locally a logarithmic branchpoint. At -2 every branch of tetration, like those of the logarithm, falls to an infinite value. since tet(-3)= log(tet(-2)) and logarithm of infinity, whatever infinity it is, is a kind of essential infinity, so every branch of tetration has these singularities we can repeat this process to get more than one singularities for every branch of tetration, which an entire pentation must avoid, so any entire pentation is trivial, a constant function pen(z) = fixed point of tet(z).

so pentations that we like won't be entire.
Reply


Messages In This Thread
RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by Base-Acid Tetration - 10/17/2009, 09:29 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  pentation and hexation sheldonison 9 6,104 7 hours ago
Last Post: sheldonison
  Approximation to half-iterate by high indexed natural iterates (base on ShlThrb) Gottfried 1 127 09/09/2019, 10:50 PM
Last Post: tommy1729
  [MSE] Shape of orbit of iterations with base b on Shell-Thron-region Gottfried 3 243 08/18/2019, 02:22 PM
Last Post: sheldonison
  Complex Tetration, to base exp(1/e) Ember Edison 7 887 08/14/2019, 09:15 AM
Last Post: sheldonison
  b^b^x with base 0<b<e^-e have three real fixpoints Gottfried 1 1,956 11/07/2017, 11:06 AM
Last Post: sheldonison
Question Analytic matrices and the base units Xorter 2 2,038 07/19/2017, 10:34 AM
Last Post: Xorter
  Base units Xorter 0 1,111 01/22/2017, 10:29 PM
Last Post: Xorter
  An explicit series for the tetration of a complex height Vladimir Reshetnikov 13 10,344 01/14/2017, 09:09 PM
Last Post: Vladimir Reshetnikov
  Is bounded tetration is analytic in the base argument? JmsNxn 0 1,136 01/02/2017, 06:38 AM
Last Post: JmsNxn
  Are tetrations fixed points analytic? JmsNxn 2 2,507 12/14/2016, 08:50 PM
Last Post: JmsNxn



Users browsing this thread: 1 Guest(s)