© 2015 Taylor & Francis. We present two case studies in one-dimensional dynamics concerning the discretization of transcritical (TC) and pitchfork (PF) bifurcations. In the vicinity of a TC or PF bifurcation point and under some natural assumptions on the one-step discretization method of order (Formula presented.) , we show that the time- (Formula presented.) exact and the step-size- (Formula presented.) discretized dynamics are topologically equivalent by constructing a two-parameter family of conjugacies in each case. As a main result, we prove that the constructed conjugacy maps are (Formula presented.) -close to the identity and these estimates are optimal.
|Original language||English (US)|
|Number of pages||42|
|Journal||Journal of Difference Equations and Applications|
|State||Published - Jan 7 2015|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): FIC/2010/05 – 2000000231
Acknowledgements: The project was supported by the European Union and co-financed by the European Social Fund
This publication acknowledges KAUST support, but has no KAUST affiliated authors.