The repeller associated with the renormalization dynamics of the spectral problem of a hierarchical tight-binding Schrodinger equation is studied. Analysis of escaping regions and of stable and unstable manifolds provide complementary descriptions of the recurrent set, whose structure undergoes relevant changes when the growth rate R of the potential barriers is modified. The minimal region containing the repeller is determined and the mechanism originating a Cantor set structure along the unstable manifold is revealed. The repeller is continuous along the stable manifold for R < 2. Finally, we show the existence of a pointlike component of the spectrum located at its upper extremum for R < 1 and we present the associated wavefunctions.
|Number of pages||20|
|Journal||Journal of Statistical Physics|
|Publication status||Published - Oct 1991|
- STRANGE REPELLERS
- SCHRODINGER OPERATOR
- HIERARCHICAL STRUCTURES
- RENORMALIZATION GROUP