Analytic theory of global bifurcation

By Boris Buffoni, J. Toland. 2003

232 citations recorded by the source corpus.

Subfields: Earth-Surface Processes, Mechanics of Materials, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/31563601d69de644e09c314d8271be7ddee45d66

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In Earth-Surface Processes

In Mechanics of Materials

In Statistical and Nonlinear Physics

Citations in the corpus

Steady Periodic Water Waves with Constant Vorticity: Regularity and Local Bifurcation (2009, methodology): “This is in striking contrast to the extensively studied irrotational case [7, 31, 36], for which any wave profile is necessarily the graph of a function and there can be no critical layers in the fluid [37, 40, 41].”
Dynamics and bifurcations of nonsmooth systems: A survey (2012, methodology): “Attempts to apply Buffoni-Dancer-Toland global analytic bifurcation theory (see Dancer [95] and Buffoni-Toland [65]) proved to be effective for studying the existence of steady waves of the Euler”
Global bifurcation of steady gravity water waves with critical layers (2014, methodology): “In [6], assumption (H4) is replaced by the slightly stronger assumption that all bounded and closed subsets (in R × X) of {(λ, u) ∈ O : F (λ, u) = 0} are compact.”
On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation (2016, methodology): “The first part is attained via analytic global bifurcation theory developed by Buffoni, Dancer and Toland [5], where we rule out all alternatives along the main bifurcation curve but maxϕ → µ/2, including in particular that the curve could return to a line of constant, but nonzero, solutions (see Fi”
Analyticity of periodic traveling free surface water waves with vorticity (2011, background): “By the implicit function theorem for real-analytic maps [3] we now conclude the existence of some ε > 0 and some φ ∈ A((−ε, ε),O) such that in a sufficiently small neighbourhood of (h0, 0) ∈ X × R all solutions of Φ(h, a) = 0 are given by (h, a) = (φ(a), a).”