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Viscosity matrices for two‐dimensional nonlinear hyperbolic systems
Author(s) -
Conley Charles C.,
Smoller Joel A.
Publication year - 1970
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160230603
Subject(s) - citation , mathematics , nonlinear system , mathematical economics , library science , algebra over a field , pure mathematics , computer science , physics , quantum mechanics
summary:This paper concerns the global structure of planar systems. It is shown that if a positively bounded system with two singular points has no closed orbits, the set of all bounded solutions is compact and simply connected. Also it is shown that for such a system the existence of connecting orbits is tightly related to the behavior of homoclinic orbits. A necessary and sufficient condition for the existence of connecting orbits is given. The number of connecting orbits is also discussed