Transversal mappings and flows

By R. Abraham, Joel W. Robbin. 2008

288 citations recorded by the source corpus.

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LECTURES ON THE MORSE COMPLEX FOR INFINITE-DIMENSIONAL MANIFOLDS (2006, background): “A classical reference for these topics is Abraham and Robbin (1967). If”
Loops and branches of coexistence states in a Lotka-Volterra competition model (2006, methodology): “3], applying the parametric transversality [1,16] to the map”
Geodesic flows with positive topological entropy, twist maps and hyperbolicity (2010, background): “1 in [1] there is a residual set DT R(1).”
On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport (2018, methodology): “By applying Morse-Sard’s lemma [1], it is anyways fulﬁlled if the function in question is d − 1 times continuously differentiable.”
On the Regularity of the Composition of Diffeomorphisms (2011, methodology): “Indeed, as u, δu ∈ C(R,R) we see that for any x ∈ R these integrands are continuous functions of t ∈ [0, 1].”
METRIC REGULARITY—A SURVEY PART 1. THEORY (2016, background): “For a proof of a ‘full’ Sard theorem see [1]; a much shorter proof for C∞ functions can be found in [82].”
A Theory of Regular Markov Perfect Equilibria in Dynamic Stochastic Games: Genericity, Stability, and Purification (2008, background): “See Mas-Colell, Whinston, and Green (1995) for an intuitive discussion and applications in economics and Abraham and Robbin (1967) and Guillemin and Pollack (1974) for further results and technical details.”