Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Continuous iteration from fixed points of base e
I think all of us could use a course in analytic continuation. Some of the things we're talking about in this thread rely heavily on theorems and terminology in analytic continuation theory. Some other related subjects include cohomology theory, fiber bundles, sheaf theory, and Riemann surfaces.

I think if we at least use the right terms, then we could all understand a little more. For example, different parts of the analytic continuation of a power series to its corresponding Riemann surface are not called "the logarithmic landscape" but could instead be called germs or sections.

There might even be nice formulas for analytic continuation, easily found if only we knew to search for "X theorem", since search terms can be a desicive factor in how successful a search is. I'm not sure if I can suggest anything in particular, but it certainly seems as if a little bit of rigor would do us some good.

Andrew Robbins

PS. A circle is a parametric plot of two sinusoidal functions. For concepts similar to a function, but impossible to describe with a function, see bipartite graph (and for self-maps, disjoint unions allow ).

Messages In This Thread
RE: Continuous iteration from fixed points of base e - by andydude - 10/16/2007, 06:21 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Are tetrations fixed points analytic? JmsNxn 2 2,734 12/14/2016, 08:50 PM
Last Post: JmsNxn
  Possible continuous extension of tetration to the reals Dasedes 0 1,229 10/10/2016, 04:57 AM
Last Post: Dasedes
  Removing the branch points in the base: a uniqueness condition? fivexthethird 0 1,459 03/19/2016, 10:44 AM
Last Post: fivexthethird
  Derivative of exp^[1/2] at the fixed point? sheldonison 10 9,590 01/01/2016, 03:58 PM
Last Post: sheldonison
  [MSE] Fixed point and fractional iteration of a map MphLee 0 2,017 01/08/2015, 03:02 PM
Last Post: MphLee
  [Update] Comparision of 5 methods of interpolation to continuous tetration Gottfried 30 27,512 02/04/2014, 12:31 AM
Last Post: Gottfried
  tetration from alternative fixed point sheldonison 21 27,302 12/06/2011, 02:43 PM
Last Post: sheldonison
  Iteration series: Different fixpoints and iteration series (of an example polynomial) Gottfried 0 2,762 09/04/2011, 05:59 AM
Last Post: Gottfried
  Fractional iteration of x^2+1 at infinity and fractional iteration of exp bo198214 10 16,012 06/09/2011, 05:56 AM
Last Post: bo198214
  attracting fixed point lemma sheldonison 4 9,241 06/03/2011, 05:22 PM
Last Post: bo198214

Users browsing this thread: 2 Guest(s)