2,534 reputation
823
bio website pcwww.liv.ac.uk/~lrempe
location Liverpool
age 37
visits member for 5 years, 7 months
seen 10 hours ago
Professor of Pure Mathematics at the University of Liverpool

Aug
24
awarded  Nice Answer
Aug
24
comment Reference request: natural extensions of topological dynamical systems
Is Proposition 3.5 in the paper "Topological mixing and uniquely ergodic systems" by Lehrer relevant? tau.ac.il/~lehrer/Papers/topological%20mixing.pdf
Aug
24
comment Is there a dynamical system such that every orbit is either periodic or dense?
I don't believe a rational map can have every orbit finite or dense, unless I am missing something. For example, there are always plenty of hyperbolic Cantor sets of nonzero Hausdorff dimension. Of course, you can have almost every point dense, but that is not the question here.
Aug
24
comment Approximation of topological dynamical systems?
Another situation that comes to mind is the convergence of families of unicritical polynomials, parameterised as $z\mapsto (1+z/d)^d+c$, to the exponential family $z\mapsto e^z+c$. The convergence seems "dynamical" in a certain sense. There is an old preprint by Devaney-Goldberg-Hubbard, now published in two parts with additional co-authors. Also, additional results in a similar spirit by Kriete, Krauskopf and others; see arxiv.org/abs/0910.0743 by my former student Helena Mihaljević-Brandt. However, I am not sure this "dynamical convergence" has ever been fully formalised as a concept.
Aug
24
revised Countable path-connected Hausdorff space
Added reference, and corrected some inaccuracies.
Aug
21
comment constructing koenigs function
@james.nixon This is absolutely standard - although as Alex points out, some of the hypotheses in your question are rather odd. (If your function sends an open subset of the plane to itself that omits more than two points, then it cannot have a repelling fixed point in that set.) Since the construction of the Koenigs function is a local one, it does not matter whether you consider attracting or repelling points; one is obtained from the other by taking inverses. Of course, the formula for the limit is exactly the one you would expect.
Aug
21
answered Is there a reference for “computing $\pi$” using external rays of the Mandelbrot set?
Aug
21
comment Hausdorff dimension of higher powers of the Mandebrot set ?
Indeed - and by universality of the Mandelbrot and Mulitbrot sets (proved by McMullen), the same will be true in any non-trivial one-dimensional family you can think up.
Aug
21
answered Countable path-connected Hausdorff space
Aug
21
comment Approximation of topological dynamical systems?
Of course, there are situations where you may not have structural stability, but still have "dynamical convergence" along certain sequence. For example, as pointed out below, the Julia set of a quadratic polynomial is not continuous at c=1/4. However, if you approach through the interval $c\in (0,1/4)$, then the Julia sets will converge (and the maps are even topologically conjugate on the Julia set - where they are topologically just the doubling map on the circle).
Aug
21
comment Approximation of topological dynamical systems?
You may be looking for the notion of Structural Stability: en.wikipedia.org/wiki/Structural_stability
Aug
21
comment Listing ORCiD in LaTeX papers
FWIW, I think may nonetheless add my ORCiD - and MR ID - to the author address information for future papers. It is a simple solution that requires virtually no work (since this does not change from one paper to the next), and the worst that can happen is for it to be ignored.
Aug
21
comment Listing ORCiD in LaTeX papers
That link with existing integrations is very helpful - I am embarrassed that I did not notice it myself before. The comment about conversion to XML is interesting - is it really true that journals (even those publishing mainly mathematics) do this? I would guess that at least the AMS probably doesn't, but they may be in the minority.
Aug
21
accepted Listing ORCiD in LaTeX papers
Aug
21
comment Listing ORCiD in LaTeX papers
@ChristianClason A potential benefit of a standard author identifier even for those who fall entirely within the scope of MR is through integration with unviersity systems. Each year all our researchers have to enter their publications into a system for the purpose of annual review, and it is an absolute pain (it doesn't help that the system changes regularly ...). If this could be populated automatically, it would be much easier. They'll never integrate with MSN for just one department, but with a universal system there is a chance - and indeed it seems some universities might already do so.
Aug
21
comment Listing ORCiD in LaTeX papers
@ChristianClason You are right that the MR author identifier is outstanding, and is maintained manually. In the more applied areas of mathematics, or in mathematical physics, there will however be plenty of people for whom not all papers are captured by MR, so a field-independent identifier should benefit them.
Aug
21
comment Listing ORCiD in LaTeX papers
@ChristianClason Ha - touché. Federico makes a good point though - and thanks to him, I have finally been bothered to notice and activate the "unsubscribe" button on the ResearchGate emails. :)
Aug
19
awarded  Nice Question
Aug
19
revised Listing ORCiD in LaTeX papers
edited the question to be more factual
Aug
19
comment Listing ORCiD in LaTeX papers
FWIW - I think a good question explains why the poster is interested in it, and some enthusiasm hardly makes it "spam". I have no connections to the ORCiD system, apart from being a user (and having felt for a while that such a system was long overdue).