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The Role of the Tangent Mapping in Analyzing Bifurcation Behaviour
Author(s) -
Fink J. P.,
Rheinboldt W. C.
Publication year - 1984
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19840640908
Subject(s) - tangent , bifurcation , nonlinear system , bifurcation theory , computation , mathematics , tangent space , connection (principal bundle) , mathematical analysis , tangent vector , singular point of a curve , differential equation , feature (linguistics) , geometry , algorithm , physics , quantum mechanics , linguistics , philosophy
Abstract In the study of solution manifolds of parameter‐dependent nonlinear equations extended systems of equations play an important role, especially for the computation of singular points, such as turning points, bifurcation points, etc. Various extended systems have been proposed in the literature. Here it is shown that a central feature in the construction of extended systems is the tangent map of differential geometry. A theory of extended equations based on the tangent map is presented which also exhibits the close connection with the choice of local coordinate systems. The ideas and results are illustrated with an example of a continuously stirred chemical reactor.