Dynamics of maps with nilpotent Jacobians
- 1 January 2006
- journal article
- research article
- Published by Taylor & Francis in Journal of Difference Equations and Applications
- Vol. 12 (1) , 49-56
Abstract
The Discrete Markus-Yamabe Conjecture (also known as the LaSalle Conjecture) imposed conditions on the Jacobian eigenvalues of a map in the hope of ensuring global attractivity of the fixed point. This paper pushes such assumptions to their extreme; the Jacobian is assumed to be nilpotent at all points. The dynamics of such maps is studied and diverse behaviour is observed, from the quick collapse of points to a globally attractive fixed point, to maps with self-intersecting invariant curves.Keywords
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