# American Institute of Mathematical Sciences

August  2013, 33(8): 3543-3554. doi: 10.3934/dcds.2013.33.3543

## Discretization of dynamical systems with first integrals

 1 Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynská dolina, 842 48 Bratislava 2 Centre for Research and Utilization of Renewable Energy, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 3058/10, 616 00 Brno, Czech Republic

Received  May 2012 Revised  September 2012 Published  January 2013

We find conditions under which the first integral of an ordinary differential equation becomes a discrete Lyapunov function for its numerical discretization. This result is applied for precluding periodic and bounded orbits under discretization for several cases.
Citation: Michal Fečkan, Michal Pospíšil. Discretization of dynamical systems with first integrals. Discrete & Continuous Dynamical Systems, 2013, 33 (8) : 3543-3554. doi: 10.3934/dcds.2013.33.3543
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