Article Contents
Article Contents

# Generalized exchange lemmas and orbits heteroclinic to invariant manifolds

• The construction of orbits with specific asymptotic properties, such as orbits that are heteroclinic or homoclinic to certain invariant sets, involves tracking stable and unstable manifolds around the system's phase space. This work addresses how, in some generality, the tracking can be achieved during the passage near a distinguished invariant manifold in the phase space. This leads to a very general form of the Exchange Lemma and it is further shown how the lemma can be used in the construction of distinguished homoclinic and heteroclinic orbits.
Mathematics Subject Classification: Primary: 34C37; Secondary: 34C26.

 Citation: