mike3 a écrit :

On Nov 6, 12:32 am, Denis Feldmann <denis.feldmann.asuppri...@club-
internet.fr> wrote:
mike3
I am sorry, but you have to go really into the math there (and I am not
sure you want to do the effort) . The answer here, for instance, is the
exact value of g'(c), where c is a Misiurewicz point and g =f^(n), with
f(z)= z^2+z.

Well, if you could tell me where I could get started, then I might go
and undertake the effort.

The paper by Tan Lei is probably too hard (but the book is not). Try
the references given athttp://en.wikipedia.org/wiki/Mandelbrot_set#References(especiallyhttp://citeseer.ist.psu.edu/cache/papers/cs/28564/http:zSzzSzwww.math...
, but even this may be quite hard...)

On Nov 6, 3:50 am, Denis Feldmann <denis.feldmann.asuppri...@club-
internet.fr> wrote:
mike3 a écrit :

On Nov 6, 12:32 am, Denis Feldmann <denis.feldmann.asuppri...@club-
internet.fr> wrote:
mike3
I am sorry, but you have to go really into the math there (and I am not
sure you want to do the effort) . The answer here, for instance, is the
exact value of g'(c), where c is a Misiurewicz point and g =f^(n), with
f(z)= z^2+z.
Well, if you could tell me where I could get started, then I might go
and undertake the effort.
The paper by Tan Lei is probably too hard (but the book is not). Try
the references given athttp://en.wikipedia.org/wiki/Mandelbrot_set#References(especiallyhttp://citeseer.ist.psu.edu/cache/papers/cs/28564/http:zSzzSzwww.math...
, but even this may be quite hard...)

"Too hard"? It depends on how much math one knows. So where
could I learn the necessary math?

mike3 a écrit :



On Nov 6, 3:50 am, Denis Feldmann <denis.feldmann.asuppri...@club-
internet.fr> wrote:
mike3 a écrit :

On Nov 6, 12:32 am, Denis Feldmann <denis.feldmann.asuppri...@club-
internet.fr> wrote:
mike3
I am sorry, but you have to go really into the math there (and I am not
sure you want to do the effort) . The answer here, for instance, is the
exact value of g'(c), where c is a Misiurewicz point and g =f^(n), with
f(z)= z^2+z.
Well, if you could tell me where I could get started, then I might go
and undertake the effort.
The paper by Tan Lei is probably too hard (but the book is not). Try
the references given athttp://en.wikipedia.org/wiki/Mandelbrot_set#References(especiallyhttp......
, but even this may be quite hard...)

"Too hard"? It depends on how much math one knows. So where
could I learn the necessary math?

Depends of what you know. Usual prerequisites are complex analysis (at
least integration, residues, etc., but it might go up to potential
theory), topology (metric spaces only ) and a few simple ideas on
iteration. But the math from there, while not really deep, can be quite
hard...

On Nov 7, 4:11 am, Denis Feldmann <denis.feldmann.asuppri...@club-
internet.fr> wrote:
mike3 a écrit :



On Nov 6, 3:50 am, Denis Feldmann <denis.feldmann.asuppri...@club-
internet.fr> wrote:
mike3 a écrit :
On Nov 6, 12:32 am, Denis Feldmann <denis.feldmann.asuppri...@club-
internet.fr> wrote:
mike3
I am sorry, but you have to go really into the math there (and I am not
sure you want to do the effort) . The answer here, for instance, is the
exact value of g'(c), where c is a Misiurewicz point and g =f^(n), with
f(z)= z^2+z.
Well, if you could tell me where I could get started, then I might go
and undertake the effort.
The paper by Tan Lei is probably too hard (but the book is not). Try
the references given athttp://en.wikipedia.org/wiki/Mandelbrot_set#References(especiallyhttp......
, but even this may be quite hard...)
"Too hard"? It depends on how much math one knows. So where
could I learn the necessary math?
Depends of what you know. Usual prerequisites are complex analysis (at
least integration, residues, etc., but it might go up to potential
theory), topology (metric spaces only ) and a few simple ideas on
iteration. But the math from there, while not really deep, can be quite
hard...

What math though comes after that, anyway? You
say it's quite "hard".

As you dont answer my question... Do you know all the prerequisites I

As you dont answer my question... Do you know all the prerequisites I
mention? On the other hand, I didn't speak of Yoccoz puzzles, for
instance (see this (already quite old) Milnor conference :
http://arxiv.org/PS_cache/math/pdf/9207/9207220v1.pdf , and look at each
prerequisite : if a lot of this makes sense to you, ok...)


But I am afraid your questions on Julia qsets for c real >1/4 proves you
are not really acquainted with all those tools. A first start would be
to convince yourself that a= -1/2+ i sqrt(4c-1)/2 is a repellent point,
and why 2a is the factor giving rise to the spiral...

Denis Feldmann wrote
As you dont answer my question... Do you know all the prerequisites I
mention? On the other hand, I didn't speak of Yoccoz puzzles, for
instance (see this (already quite old) Milnor conference :
http://arxiv.org/PS_cache/math/pdf/9207/9207220v1.pdf , and look at
each prerequisite : if a lot of this makes sense to you, ok...)


But I am afraid your questions on Julia qsets for c real >1/4 proves
you are not really acquainted with all those tools. A first start
would be to convince yourself that a= -1/2+ i sqrt(4c-1)/2 is a
repellent point, and why 2a is the factor giving rise to the spiral...

Oh, yes, see also http://arxiv.org/PS_cache/math/pdf/9905/9905169v1.pdf
for a typical example of the use of potential theory.

mike3 a écrit :



On Nov 7, 4:11 am, Denis Feldmann <denis.feldmann.asuppri...@club-
internet.fr> wrote:
mike3 a écrit :

On Nov 6, 3:50 am, Denis Feldmann <denis.feldmann.asuppri...@club-
internet.fr> wrote:
mike3 a écrit :
On Nov 6, 12:32 am, Denis Feldmann <denis.feldmann.asuppri...@club-
internet.fr> wrote:
mike3
I am sorry, but you have to go really into the math there (and I am not
sure you want to do the effort) . The answer here, for instance, is the
exact value of g'(c), where c is a Misiurewicz point and g =f^(n), with
f(z)= z^2+z.
Well, if you could tell me where I could get started, then I might go
and undertake the effort.
The paper by Tan Lei is probably too hard (but the book is not). Try
the references given athttp://en.wikipedia.org/wiki/Mandelbrot_set#References(especiallyhttp......
, but even this may be quite hard...)
"Too hard"? It depends on how much math one knows. So where
could I learn the necessary math?
Depends of what you know. Usual prerequisites are complex analysis (at
least integration, residues, etc., but it might go up to potential
theory), topology (metric spaces only ) and a few simple ideas on
iteration. But the math from there, while not really deep, can be quite
hard...

What math though comes after that, anyway? You
say it's quite "hard".

As you dont answer my question... Do you know all the prerequisites I
mention? On the other hand, I didn't speak of Yoccoz puzzles, for
instance (see this (already quite old) Milnor conference :http://arxiv.org/PS_cache/math/pdf/9207/9207220v1.pdf, and look at each
prerequisite : if a lot of this makes sense to you, ok...)

But I am afraid your questions on Julia qsets for c real >1/4 proves you
are not really acquainted with all those tools. A first start would be
to convince yourself that a= -1/2+ i sqrt(4c-1)/2 is a repellent point,
and why 2a is the factor giving rise to the spiral...

On Nov 8, 1:06 am, Denis Feldmann <denis.feldmann.asuppri...@club-
internet.fr> wrote:
mike3 a écrit :



What math though comes after that, anyway? You
say it's quite "hard".
As you dont answer my question... Do you know all the prerequisites I
mention? On the other hand, I didn't speak of Yoccoz puzzles, for
instance (see this (already quite old) Milnor conference :http://arxiv.org/PS_cache/math/pdf/9207/9207220v1.pdf, and look at each
prerequisite : if a lot of this makes sense to you, ok...)

But I am afraid your questions on Julia qsets for c real >1/4 proves you
are not really acquainted with all those tools. A first start would be
to convince yourself that a= -1/2+ i sqrt(4c-1)/2 is a repellent point,
and why 2a is the factor giving rise to the spiral...

But you seem to suggest getting a good acquaintance with the tools
is "hard". Why is that?

mike3 a écrit :
snip
Why what? Do you know the tools? If you do, you know if they were hard
to acquire or not (for you).

If you dont, why are you asking?

Anyway,
all this is getting ridiculous, as you never answer the key question :
what do you know already ? Compared with, say, what you need to know to
understand Wiles' proof, the tools needed to understand the Mandelbrot
set are quite easy (I would say 5/6 years of university...) On the other
hand, if you dont even know some complex analysis, understanding, say,
external rays (http://en.wikipedia.org/wiki/External_ray) may become
quite a challenge...

On Nov 11, 11:29 pm, Denis Feldmann <denis.feldmann.asuppri...@club-
internet.fr> wrote:
mike3 a écrit :
snip
Why what? Do you know the tools? If you do, you know if they were hard
to acquire or not (for you).

Well, I'm not sure if I know _all_ the tools, but I do know
something about complex calculus/analysis (basic integration/
differentiation), and a little about topology. However
it's getting beyond that point that's the rub.

How much would it cost for a good university course like that
anyway, and how can I get the money, having not been born into
wealth (currently I'm pretty poor. CURRENTLY, that is.)?
How do you get rich? I guess that's what I'm really after --
I want to get rich, so I can study this stuff REAL
deep -- and it's not just math stuff.

I noticed something looking at that page, by the way. The paths
followed by those "external rays" look like the same paths
followed by ornaments coming off midgets! Is there a relationship
there?