TY - JOUR

T1 - Eikonal algebra on a graph of simple structure

AU - Белишев, Михаил Игоревич

AU - Каплун, Александр Владимирович

N1 - Funding Information: The authors are extremely grateful to I.V.Kubyshkin for kind assistance in computer graphics. The work is supported by the RFBR grant 18-01-00269.

PY - 2018/9

Y1 - 2018/9

N2 - An eikonal algebra C(black-letters)(Ω) is a C*-algebra related to a metric graph Ω. It is determined by trajectories and reachable sets of a dynamical system associated with the graph. The system describes the waves, which are initiated by boundary sources (controls) and propagate into the graph with finite velocity. Motivation and interest to eikonal algebras comes from the inverse problem of reconstruction of the graph via its dynamical and/or spectral boundary data. Algebra C(black-letters)(Ω) is determined by these data. In the mean time, its structure and algebraic invariants (irreducible representations) are connected with topology of Ω. We demonstrate such connections and study C(black-letters)(Ω) by the example of Ω of a simple structure. Hopefully, in future, these connections will provide an approach to reconstruction.

AB - An eikonal algebra C(black-letters)(Ω) is a C*-algebra related to a metric graph Ω. It is determined by trajectories and reachable sets of a dynamical system associated with the graph. The system describes the waves, which are initiated by boundary sources (controls) and propagate into the graph with finite velocity. Motivation and interest to eikonal algebras comes from the inverse problem of reconstruction of the graph via its dynamical and/or spectral boundary data. Algebra C(black-letters)(Ω) is determined by these data. In the mean time, its structure and algebraic invariants (irreducible representations) are connected with topology of Ω. We demonstrate such connections and study C(black-letters)(Ω) by the example of Ω of a simple structure. Hopefully, in future, these connections will provide an approach to reconstruction.

KW - C-algebra of eikonals

KW - Hyperbolic dynamical system

KW - Metric graph

KW - Reachable sets

UR - http://www.scopus.com/inward/record.url?scp=85055743041&partnerID=8YFLogxK

M3 - Article

VL - 6

SP - 4

EP - 33

JO - Eurasian Journal of Mathematical and Computer Applications

JF - Eurasian Journal of Mathematical and Computer Applications

SN - 2306-6172

IS - 3

M1 - 1

ER -