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717
bio website pcwww.liv.ac.uk/~lrempe
location Liverpool
age 36
visits member for 4 years, 10 months
seen 12 mins ago
Professor of Pure Mathematics at the University of Liverpool

21h
revised A question on deficient values of entire functions
Corrected spelling and grammar.
22h
suggested suggested edit on A question on deficient values of entire functions
22h
answered A question on deficient values of entire functions
1d
revised Is there an (almost) dense set of quadratic polynomials which is not in the interior of the Mandelbrot set?
Extended the answer.
1d
revised Is there an (almost) dense set of quadratic polynomials which is not in the interior of the Mandelbrot set?
Slightly reformulated the question to make it more descriptive. Fixed some grammar/wording, and tried to add some clarification (hopefully without changing the intention of the author or basic structure of the question).
1d
suggested suggested edit on Is there an (almost) dense set of quadratic polynomials which is not in the interior of the Mandelbrot set?
1d
answered Is there an (almost) dense set of quadratic polynomials which is not in the interior of the Mandelbrot set?
Nov
2
comment 13 months and not even one report. what would you do?
Know it's a bit late, but glad to hear that things worked out.
Nov
2
answered Failure of Mostow rigidity in dim. 2
Oct
31
answered Is it possible to define the density of the logistic map for $x<0$?
Oct
27
comment Clustering of periodic points for a polynomial iteration of $\mathbb{C}$
@VesselinDimitrov Yes, that's what I took your first comment to mean. Interestingly, using recent work on 'near-parabolic renormalization', it could be possible to quantify the above construction, and hence - combined with your observation - give estimates on the combinatorics (i.e., the numbers $q_j$) that ensure that the resulting parameter is transcendental. That could be a publishable result, although depending on the technical work needed it may or may not be worthwhile to work it out. Davoud Cheraghi (Imperial College) is a world expert on this type of argument.
Oct
26
comment Clustering of periodic points for a polynomial iteration of $\mathbb{C}$
@VesselinDimitrov that's an interesting point. The construction is a generalization of the Feigenbaum point (where we make a sequence of period 2 bifurcations, and take the limit). In this case, I believe that it is not known whether the limit parameter is transcendental. (More generally, one could ask whether every infinitely renormalizable parameter is transcendental.)
Oct
26
comment A forked plane continuum
Nice question. I suspect that the answer is no, i.e. a continuum may exist that violates your requirement. I would try to construct it as a nested intersection of continua $K_n$, where every subcontinuum of $K_n$ that contains both $P$ and a point in either of the two quadrants at height $q_n$ must also contain a point at the same height in the other quadrant. Here $q_n$ is a sequence that is dense in the interval $[0,1]$. The construction in each step would be based on a thickened version of the $\sin(1/x)$-continuum. I cannot claim to have thought out the details, so this may not work ...
Oct
26
answered Clustering of periodic points for a polynomial iteration of $\mathbb{C}$
Oct
16
comment Conditions conformal mapping to be expansive
@ChrisJudge, I have elaborated further. Hope this makes sense.
Oct
16
revised Conditions conformal mapping to be expansive
added further detail and ideas to the answer
Oct
16
answered Conditions conformal mapping to be expansive
Oct
2
comment Metric properties of a quadratic differential at an essential singularity
How do you conclude your inequality? After all, there may well be some places where $f$ is much smaller than the corresponding term in the Laurent series, so it seems that you need to give some justification.
Sep
30
awarded  Explainer
Sep
19
comment Continuous extension of Riemann maps and the Caratheodory-Torhorst Theorem
@MalikYounsi However, prime end theory is relevant in dynamics; for example, I think that it is implicitly used in Perez-Marco's hedgehog theory to construct the analytic circle diffeomorphism associated to hedgehog dynamics. (One observes that the induced map on a one-sided neighbourhood of the unit circle extends continuously, and then applies Schwarz reflection.) Also, I think it was used in Sullivan's original proof of the no-wandering domains theorem, though I may misremember.