# American Institute of Mathematical Sciences

May  2008, 9(3&4, May): 431-461. doi: 10.3934/dcdsb.2008.9.431

## Heteroclinic connections in singularly perturbed systems

 1 Dipartimento di Scienze Matematiche, Facoltà di Ingegneria, Università, Via Brecce Bianche, 1, 60100 Ancona, Italy 2 Department of Mathematics, National Taiwan University, Taipei 106, Taiwan

Received  October 2006 Revised  July 2007 Published  February 2008

We consider a singularly perturbed system with two normally hyperbolic centre manifolds. We derive one bifurcation function, the zeros of which correspond to heteroclinic connections near such a connection for the unperturbed system, and a second bifurcation function the zeros of which correspond to the vectors in the intersection of the tangent spaces to the centre-unstable and centre-stable manifolds along the heteroclinic connections.
Citation: Flaviano Battelli, Ken Palmer. Heteroclinic connections in singularly perturbed systems. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 431-461. doi: 10.3934/dcdsb.2008.9.431
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