Zobrazeno 1 - 10
of 36
pro vyhledávání: '"Anton Gorodetski"'
Autor:
Anton Gorodetski, Alexandro Luna
Publikováno v:
Dynamical Systems. 38:268-274
We study the space of ergodic measures of the map $$f:\mathbb{T}^2\to \mathbb{T}^2, \ f(x, y)=(x, \ x+y)(\text{mod}\, 1),$$ and show that its structure is similar to the graph of Thomae's function.
Comment: 6 pages, 2 figures
Comment: 6 pages, 2 figures
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7336f3bca4183e2991d449fe1d795544
https://doi.org/10.1080/14689367.2023.2174000
https://doi.org/10.1080/14689367.2023.2174000
Autor:
David Damanik, Anton Gorodetski
Publikováno v:
Communications in Mathematical Physics. 393:1583-1613
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::eb7659385c791f159083abb45647aea3
https://doi.org/10.1007/s00220-022-04395-w
https://doi.org/10.1007/s00220-022-04395-w
Autor:
Anton Gorodetski, David Damanik
Publikováno v:
Journal of Spectral Theory, vol 8, iss 4
Author(s): Damanik, D; Gorodetski, A | Abstract: We study the spectrum and the density of states measure of the square Fibonacci Hamiltonian. We describe where the transitions from positive-measure to zero-measure spectrum and from absolutely continu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::90e3084927e601b1e04527ad8331da0e
https://doi.org/10.4171/jst/232
https://doi.org/10.4171/jst/232
Publikováno v:
Journal of Functional Analysis. 280:108911
We construct multidimensional Schrodinger operators with a spectrum that has no gaps at high energies and that is nowhere dense at low energies. This gives the first example for which this widely expected topological structure of the spectrum in the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::629876f972d0e3974cd26d1185df30b5
https://doi.org/10.1016/j.jfa.2020.108911
https://doi.org/10.1016/j.jfa.2020.108911
Autor:
Victor Kleptsyn, Anton Gorodetski
Publikováno v:
Advances in Mathematics. 378:107522
We consider random products of S L ( 2 , R ) matrices that depend on a parameter in a non-uniformly hyperbolic regime. We show that if the dependence on the parameter is monotone then almost surely the random product has upper (limsup) Lyapunov expon
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5d63ef4d71b06c9ea75e79e3fa3a3c7f
https://doi.org/10.1016/j.aim.2020.107522
https://doi.org/10.1016/j.aim.2020.107522
Publikováno v:
Annales Henri Poincare, vol 20, iss 4
Annales Henri Poincaré, vol 20, iss 4
Annales Henri Poincaré, vol 20, iss 4
We construct multidimensional almost-periodic Schr\"odinger operators whose spectrum has zero lower box counting dimension. In particular, the spectrum in these cases is a generalized Cantor set of zero Lebesgue measure.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e177b08f79af2eceecc16d66c7aa2701
http://arxiv.org/abs/1809.02720
http://arxiv.org/abs/1809.02720
Autor:
Anton Gorodetski, Scott Northrup
Publikováno v:
Fundamenta Mathematicae, vol 240, iss 3
Gorodetski, A; & Northrup, S. (2018). On sums of nearly affine Cantor sets. FUNDAMENTA MATHEMATICAE, 240(3), 205-219. doi: 10.4064/fm183-3-2017. UC Irvine: Retrieved from: http://www.escholarship.org/uc/item/3vd207v7
Gorodetski, A; & Northrup, S. (2018). On sums of nearly affine Cantor sets. FUNDAMENTA MATHEMATICAE, 240(3), 205-219. doi: 10.4064/fm183-3-2017. UC Irvine: Retrieved from: http://www.escholarship.org/uc/item/3vd207v7
For a compact set $K\subset \mathbb{R}^1$ and a family $\{C_\lambda\}_{\lambda\in J}$ of dynamically defined Cantor sets sufficiently close to affine with $\text{dim}_H\, K+\text{dim}_H\, C_\lambda>1$ for all $\lambda\in J$, under natural technical c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e59d568da0fd42f3c9798cb5c3cd27de
https://escholarship.org/uc/item/3vd207v7
https://escholarship.org/uc/item/3vd207v7
Autor:
Yakov Pesin, Anton Gorodetski
Author(s): Gorodetski, A; Pesin, Y | Abstract: We show that the space of hyperbolic ergodic measures of a given index supported on an isolated homoclinic class is path connected and entropy dense provided that any two hyperbolic periodic points in th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b066788d9c9ed170e36781fd8410f6cb
https://escholarship.org/uc/item/5sw8g3qt
https://escholarship.org/uc/item/5sw8g3qt
Publikováno v:
Moscow Mathematical Journal. 14:290-308
We consider a minimal action of a finitely generated semigroup by homeomorphisms of a circle, and show that the collection of translation numbers of individual elements completely determines the set of generators (up to a common continuous change of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8ad4b88b190fc8c817886cdfcf9aeb9f
https://doi.org/10.17323/1609-4514-2014-14-2-290-308
https://doi.org/10.17323/1609-4514-2014-14-2-290-308
Publikováno v:
Inventiones Mathematicae, vol 206, iss 3
Damanik, D; Gorodetski, A; & Yessen, W. (2016). The Fibonacci Hamiltonian. INVENTIONES MATHEMATICAE, 206(3), 629-692. doi: 10.1007/s00222-016-0660-x. UC Irvine: Retrieved from: http://www.escholarship.org/uc/item/04p6f10m
Damanik, D; Gorodetski, A; & Yessen, W. (2016). The Fibonacci Hamiltonian. INVENTIONES MATHEMATICAE, 206(3), 629-692. doi: 10.1007/s00222-016-0660-x. UC Irvine: Retrieved from: http://www.escholarship.org/uc/item/04p6f10m
We consider the Fibonacci Hamiltonian, the central model in the study of electronic properties of one-dimensional quasicrystals, and provide a detailed description of its spectrum and spectral characteristics (namely, the optimal H\"older exponent of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9f6be9fd080e156f253091ba12661518
https://escholarship.org/uc/item/04p6f10m
https://escholarship.org/uc/item/04p6f10m