Hello James,
Thanks for your analysis of my work. You are not being harsh, just honest.
Convergence - James, you are correct about there being no information on convergence in my article. Yiannis is helping out by reviewing my work with an analysis of the Faa Di Bruno algorithm. He was concerned about the weakness of my converge proofs and recommended an analytic continuation approach. Since I know the value of all the multipliers, I hope to provide an analytic continuation proof.
Convergence proofs
Complex Dynamics - I've worked out much of complex dynamics before reading about it. My approach gives a non-topological way of deriving large potions of complex dynamics. I have minimal formal education, college junior, so my understanding of higher dimensional complex dynamics is limited.
Thanks for your analysis of my work. You are not being harsh, just honest.
Convergence - James, you are correct about there being no information on convergence in my article. Yiannis is helping out by reviewing my work with an analysis of the Faa Di Bruno algorithm. He was concerned about the weakness of my converge proofs and recommended an analytic continuation approach. Since I know the value of all the multipliers, I hope to provide an analytic continuation proof.
Convergence proofs
- Combinatorial convergence - The Faa Di Bruno algorithm only produces a finite number of components whose values are finite, therefore must Faa Di Bruno converge.
- Moiré patterns - Proof by contradiction. Given two Moiré transparencies; one with infinite values and one with finite values. offsetting them creates a situation where an finite value in the first transparency becomes arbitrarily close to an infinite value in the second transparency.
- Analytic continuation - this is a well accepted way to establish convergence.
Complex Dynamics - I've worked out much of complex dynamics before reading about it. My approach gives a non-topological way of deriving large potions of complex dynamics. I have minimal formal education, college junior, so my understanding of higher dimensional complex dynamics is limited.
Daniel