What is recorded here?
Analyzed conditions under which a family of differential systems develops a periodic solution as a conjugate pair of characteristic exponents crosses the imaginary axis.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
The record is the sole-author 1942 German paper. Earlier planar results, later center-manifold formulations, normal-form coefficients and applications collectively called Hopf bifurcation remain separate.
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People and systems
Eberhard Hopf
The named authors contributed to this scoped work; individual effort shares and later applications are not assigned by the byline.
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Documented countries / regions: Germany
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English catalogue narrative
Hopf: bifurcation of a periodic solution from a stationary solution
Analyzed conditions under which a family of differential systems develops a periodic solution as a conjugate pair of characteristic exponents crosses the imaginary axis.
Scientific scope
The record is the sole-author 1942 German paper. Earlier planar results, later center-manifold formulations, normal-form coefficients and applications collectively called Hopf bifurcation remain separate.
Reading status
This is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.
People and systems
Eberhard Hopf
The named authors contributed to this scoped work; individual effort shares and later applications are not assigned by the byline.