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The absolute spectrum revisited from a topological viewpoint. (arXiv:1706.08305v1 [math.DS])
来源于:arXiv
We consider the topological relation behind the spectral behavior of a linear
operator that arises in the stability problem of traveling waves on a large
bounded domain. When the domain size tends to infinity, the absolute and
asymptotic essential spectra appears as accumulation sets of eigenvalues under
separated and periodic boundary conditions, respectively. We present new proofs
of Sandstede and Scheel [Theorems 4 and 5 of [14]] in a topological framework.
The eigenfunction induces a curve on the Grassmannian manifold. To extract
topological information from them, we decompose the Grassmannian into the
submanifolds using the Schubert cycles, and analyze the curves on each
submanifolds. 查看全文>>