Perturbing a Planar Rotation: Normal Hyperbolicity and Angular Twist

Alain Chenciner ()
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Alain Chenciner: Observatoire de Paris, IMCCE (UMR 8028), ASD

Chapter Chapter 11 in Geometry in History, 2019, pp 451-468 from Springer

Abstract: Abstract In generic two-parameter families of local diffeomorphisms of the plane unfolding a local diffeomorphism with an elliptic fixed point, the tension between radial (hyperbolic) and tangential (elliptic) behaviour gives rise to phenomena where the whole wealth of the area preserving case is unfolded along some direction of the parameter space.

Keywords: Bifurcation of invariant curves; Normal form; Normal hyperbolicity; Twist map; KAM; Resonance; 37E30; 37E40; 37D05; 34C23; 37G05; 37G15 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/978-3-030-13609-3_11

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