The Density of States Measure of the Weakly Coupled Fibonacci Hamiltonian
| dc.citation.firstpage | 976 | |
| dc.citation.journalTitle | Geometric and Functional Analysis | |
| dc.citation.lastpage | 989 | |
| dc.citation.volumeNumber | 22 | |
| dc.contributor.author | Damanik, David | |
| dc.contributor.author | Gorodetski, Anton | |
| dc.date.accessioned | 2013-09-13T16:07:08Z | |
| dc.date.available | 2013-09-13T16:07:08Z | |
| dc.date.issued | 2012 | |
| dc.description.abstract | We consider the density of states measure of the Fibonacci Hamiltonian and show that, for small values of the coupling constant V , this measure is exact-dimensional and the almost everywhere value dV of the local scaling exponent is a smooth function of V , is strictly smaller than the Hausdor dimension of the spectrum, and converges to one as V tends to zero. The proof relies on a new connection between the density of states measure of the Fibonacci Hamiltonian and the measure of maximal entropy for the Fibonacci trace map on the non-wandering set in the V -dependent invariant surface. This allows us to make a connection between the spectral problem at hand and the dimension theory of dynamical systems. | |
| dc.embargo.terms | none | |
| dc.identifier.citation | Damanik, David and Gorodetski, Anton. "The Density of States Measure of the Weakly Coupled Fibonacci Hamiltonian." <i>Geometric and Functional Analysis,</i> 22, (2012) Springer: 976-989. http://dx.doi.org/10.1007/s00039-012-0173-8. | |
| dc.identifier.doi | http://dx.doi.org/10.1007/s00039-012-0173-8 | |
| dc.identifier.uri | https://hdl.handle.net/1911/71898 | |
| dc.language.iso | eng | |
| dc.publisher | Springer | |
| dc.rights | This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer. | |
| dc.title | The Density of States Measure of the Weakly Coupled Fibonacci Hamiltonian | |
| dc.type | Journal article | |
| dc.type.dcmi | Text | |
| dc.type.publication | post-print |