Hey, MphLEE!
Yes, these diagrams would be very basic to a trained mathematician who specializes in algebra, lol. I was inspired by your diagrams... to use diagrams. Not to actually use complex graphs; like the stuff you do. Not even to broach the commutative diagram nethers. I'm not a diagrammatical person (by nature, in my mathematics, so it'd probably be worse if I did).
But In John Milnor's book Dynamics In One Complex Variable; he uses graphs of about the same complexity as mine (though I will say, mine were a little weird.) The entire purpose of the graphs is to view the morphism from a domain in \( \mathbb{L} \) to \( \mathbb{D}^\times \); while respecting the functional equation. I was thinking of my diagrams as morphisms between \( \mathbb{L} \to \mathbb{D}^\times \) while respecting \( s\mapsto s+1 \) gets mapped to \( w\mapsto e^{-\lambda}w \). And then considering the \( \log \) map; as on either/or space. Where we have a nice bounded argument on \( \tau_\lambda \) in \( \mathbb{L} \); and we can now visualize this bounded argument on \( u_\lambda \) in \( \mathbb{D}^\times \) with a different functional equation. I may not have expressed it perfectly. I only wrote the diagrams as a visual aid, not as a method of proof
It was entirely supplemental. I apologize if they're not to your standard though, lol. As far as I used them, was as a visual aid. Which, was essentially how Milnor was to me.
Thanks though, for giving the paper enough of a time of day to reply to. I hope the paper seems, at least intuitive, if not rigorous to you. By which, if you can't corroborate the technical aspects; at least, I hope the motions make sense, lol.
Thanks again, James
Yes, these diagrams would be very basic to a trained mathematician who specializes in algebra, lol. I was inspired by your diagrams... to use diagrams. Not to actually use complex graphs; like the stuff you do. Not even to broach the commutative diagram nethers. I'm not a diagrammatical person (by nature, in my mathematics, so it'd probably be worse if I did).
But In John Milnor's book Dynamics In One Complex Variable; he uses graphs of about the same complexity as mine (though I will say, mine were a little weird.) The entire purpose of the graphs is to view the morphism from a domain in \( \mathbb{L} \) to \( \mathbb{D}^\times \); while respecting the functional equation. I was thinking of my diagrams as morphisms between \( \mathbb{L} \to \mathbb{D}^\times \) while respecting \( s\mapsto s+1 \) gets mapped to \( w\mapsto e^{-\lambda}w \). And then considering the \( \log \) map; as on either/or space. Where we have a nice bounded argument on \( \tau_\lambda \) in \( \mathbb{L} \); and we can now visualize this bounded argument on \( u_\lambda \) in \( \mathbb{D}^\times \) with a different functional equation. I may not have expressed it perfectly. I only wrote the diagrams as a visual aid, not as a method of proof
It was entirely supplemental. I apologize if they're not to your standard though, lol. As far as I used them, was as a visual aid. Which, was essentially how Milnor was to me.Thanks though, for giving the paper enough of a time of day to reply to. I hope the paper seems, at least intuitive, if not rigorous to you. By which, if you can't corroborate the technical aspects; at least, I hope the motions make sense, lol.
Thanks again, James
