Hopf: bifurcation of a periodic solution from a stationary solution

What changed

Analyzed emergence of periodic solutions near an equilibrium as characteristic exponents cross.

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.

Evidence

The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. 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.

Contributors

• Eberhard Hopf · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.

• University-hosted copy of Hopf’s 1942 paper
• Max Planck bibliography for Hopf’s original paper

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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