Symplectic homogeneous diffeomorphisms, Cremona maps and the jolt representation

Published 9 February 2005 • 2005 IOP Publishing Ltd and London Mathematical Society
, , Citation Héctor E Lomelí 2005 Nonlinearity 18 1065 DOI 10.1088/0951-7715/18/3/008

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1 Department of Mathematics, Instituto Tecnológico Autónomo de México, México DF 01000, Mexico

Dates

  1. Received 16 August 2004
  2. Published

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0951-7715/18/3/1065

Abstract

We study the relation between the Jacobian conjecture and the so-called jolt map representation. We define jolt maps as any map that is symplectic-conjugate to a shear map. In particular, we study a family of homogeneous-symplectic maps and conjecture that all homogeneous-symplectic maps are jolt maps. We prove the result in the plane.

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10.1088/0951-7715/18/3/008