Zobrazeno 1 - 10
of 68
pro vyhledávání: '"Jonathan M. Fraser"'
Autor:
JONATHAN M. FRASER, ISTVÁN KOLOSSVÁRY
Publikováno v:
Ergodic Theory and Dynamical Systems. :1-23
We derive upper and lower bounds for the Assouad and lower dimensions of self-affine measures in $\mathbb{R}^d$ generated by diagonal matrices and satisfying suitable separation conditions. The upper and lower bounds always coincide for $d=2,3$ yield
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5661b70fcd72c37b73b148ad9d5c3ecc
https://doi.org/10.1017/etds.2022.64
https://doi.org/10.1017/etds.2022.64
Publikováno v:
Proceedings of the American Mathematical Society. 150:4729-4742
The 'popcorn function' isThe `popcorn function' is a well-known and important example in real analysis with many interesting features. We prove that the box dimension of the graph of the popcorn function is 4/3, as well as computing the Assouad dimen
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::49e2b7875df46cd7a0bb38801615408e
https://doi.org/10.1090/proc/15729
https://doi.org/10.1090/proc/15729
Publikováno v:
Mathematische Zeitschrift. 301:2497-2508
A $(d,k)$-set is a subset of $\mathbb{R}^d$ containing a $k$-dimensional unit ball of all possible orientations. Using an approach of D.~Oberlin we prove various Fourier dimension estimates for compact $(d,k)$-sets. Our main interest is in restricted
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dcd03d26080a81b31b7db9ad2ff9f739
https://doi.org/10.1007/s00209-022-02971-3
https://doi.org/10.1007/s00209-022-02971-3
Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying Diophantine approximation in an arbitrary totally bounded metric space where the rationals are replaced with
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::75927df4b4a30c6b11c13b8e90ae05e7
https://hdl.handle.net/10023/26529
https://hdl.handle.net/10023/26529
Publikováno v:
Nonlinearity. 34:6331-6357
We study L q -spectra of planar self-affine measures generated by diagonal matrices. We introduce a new technique for constructing and understanding examples based on combinatorial estimates for the exponential growth of certain split binomial sums.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6362ea62bde29623811185f1f9e9cc76
https://doi.org/10.1088/1361-6544/ac14a2
https://doi.org/10.1088/1361-6544/ac14a2
Autor:
Jonathan M. Fraser
Publikováno v:
Nonlinearity. 34:3251-3270
The winding problem concerns understanding the regularity of functions which map a line segment onto a spiral. This problem has relevance in fluid dynamics and conformal welding theory, where spirals arise naturally. Here we interpret `regularity' in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f593c255ec3d3dcec9ec6ca55f72727e
https://doi.org/10.1088/1361-6544/abe75e
https://doi.org/10.1088/1361-6544/abe75e
Publikováno v:
Journal of Fractal Geometry. 8:95-116
Intermediate dimensions were recently introduced to interpolate between the Hausdorff and box-counting dimensions of fractals. Firstly, we show that these intermediate dimensions may be defined in terms of capacities with respect to certain kernels.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::82f2f38c2aaf6ea1e1cc6079edefc5df
https://doi.org/10.4171/jfg/99
https://doi.org/10.4171/jfg/99
Publikováno v:
Ergodic Theory and Dynamical Systems. 41:3288-3306
We study the $L^{q}$ -spectrum of measures in the plane generated by certain nonlinear maps. In particular, we consider attractors of iterated function systems consisting of maps whose components are $C^{1+\alpha }$ and for which the Jacobian is a lo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0b20103955eb53cf4ccf60e2efff235d
https://doi.org/10.1017/etds.2020.106
https://doi.org/10.1017/etds.2020.106
Autor:
Jonathan M. Fraser, Antti Käenmäki
Publikováno v:
Proceedings of the American Mathematical Society. 148:3393-3405
We prove that for an arbitrary upper semi-continuous function $\phi\colon G(1,2) \to [0,1]$ there exists a compact set $F$ in the plane such that $\dim_{\textrm{A}} \pi F = \phi(\pi)$ for all $\pi \in G(1,2)$, where $\pi F$ is the orthogonal projecti
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::68e34e23b82e497bf8feaf17825d655e
https://doi.org/10.1090/proc/14999
https://doi.org/10.1090/proc/14999
Autor:
Haipeng Chen, Jonathan M. Fraser
Funding: The research of H. Chen was funded by China Scholarship Council (File No. 201906150102). J. M.Fraser was financially supported by an EPSRC Standard Grant (EP/R015104/1) and a Leverhulme Trust Research Project Grant (RPG-2019-034). Let pn den
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b8f6b2871a2b3ad147b6b4067865908f
https://hdl.handle.net/10023/26321
https://hdl.handle.net/10023/26321