# American Institute of Mathematical Sciences

January  2007, 18(1): 135-157. doi: 10.3934/dcds.2007.18.135

## Area contraction in the presence of first integrals and almost global convergence

 1 SYSTeMS Research Group, Dept. of Electrical Energy, Systems and Automation, Ghent University, Technologiepark-Zwijnaarde 914, 9052 Zwijnaarde, Belgium, Belgium

Received  April 2006 Revised  November 2006 Published  February 2007

We investigate the evolution of the area of multi-dimensional surfaces along the flow of a dynamical system with known first integrals, and we formulate sufficient conditions for area contraction.
These results, together with known results about the Hausdorff dimension and the box-counting dimension of invariant sets, are applied to systems exhibiting almost global convergence/asymptotic stability. This leads to a generalization of a well-known result on almost global convergence of a system, based on the use of density functions. We conclude with an example.
Citation: Dirk Aeyels, Filip De Smet, Bavo Langerock. Area contraction in the presence of first integrals and almost global convergence. Discrete & Continuous Dynamical Systems - A, 2007, 18 (1) : 135-157. doi: 10.3934/dcds.2007.18.135
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