Abstract
If g ∈ ℰ x , λ , we say that g has Z 2-symmetry if g is an odd function of x; in symbols, if
We use this terminology because we think of a two-element group Z 2 = {I, R} acting on the real line, where I is the identity and Rx = −x; equation (0.1) asserts that g commutes with the action of this group. In this chapter we study bifurcation problems with Z 2-symmetry. Bifurcation problems with this symmetry arise often in applications. For example, the buckling model of Chapter I, §1 was Z 2-symmetric; in that case the physical representation of the symmetry was reflection across the horizontal axis. Moreover, bifurcation problems of the form (0.1) play a central role in our treatment of the Hopf bifurcation in Chapter VIII.
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© 1985 Springer Science+Business Media New York
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Golubitsky, M., Schaeffer, D.G. (1985). Bifurcation with Z 2-Symmetry. In: Singularities and Groups in Bifurcation Theory. Applied Mathematical Sciences, vol 51. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5034-0_6
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DOI: https://doi.org/10.1007/978-1-4612-5034-0_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-9533-4
Online ISBN: 978-1-4612-5034-0
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