• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 All Maps Have Flows & All Hyperoperators Operate on Matrices Daniel Fellow Posts: 86 Threads: 33 Joined: Aug 2007 03/14/2020, 06:22 AM (This post was last modified: 03/14/2020, 06:31 AM by Daniel.) In 1987 Stephen Wolfram introduced me to the question of whether all maps are flows. Given the fifteen-year-old mathematics on Tetration.org, I have a simple proof that all maps are flows, that they are two different views of the same thing. Consider the Taylor series of an arbitrary smooth iterated function and it's representation as the combinatorial structure total partitions, the recursive version of set partitions. Each enumerated combinatorial structure has a symmetry associated with it. Let's say we want to consider $S_2$, just remove all combinatorial structures inconsistent with $S_2$. Because I can define $GL(n)$ as the domain and the iterant, through representation theory, that if I can compute with matrices, I can compute within any symmetry. Just as the exponential function of invertible matrices can be computed, all hyperoperations can be defined with invertible matrices. Daniel « Next Oldest | Next Newest »

 Possibly Related Threads... Thread Author Replies Views Last Post Interesting commutative hyperoperators ? tommy1729 0 1,515 02/17/2020, 11:07 PM Last Post: tommy1729 Analytic matrices and the base units Xorter 2 4,873 07/19/2017, 10:34 AM Last Post: Xorter Logic hyperoperators hixidom 0 2,594 10/14/2015, 08:26 PM Last Post: hixidom Theorem in fractional calculus needed for hyperoperators JmsNxn 5 10,828 07/07/2014, 06:47 PM Last Post: MphLee Hyperoperators [n] basics for large n dyitto 9 14,472 03/12/2011, 10:19 PM Last Post: dyitto Hyperoperators Mr. Pig 4 8,518 06/20/2010, 12:26 PM Last Post: bo198214 Matrices tetrated Gottfried 0 2,933 12/26/2008, 05:00 PM Last Post: Gottfried Eigensystem of tetration-matrices Gottfried 7 12,435 09/20/2007, 07:06 AM Last Post: Gottfried

Users browsing this thread: 2 Guest(s)