Normal hyperbolicity and unbounded critical manifolds

作者：Kuehn Christian^*

来源：Nonlinearity, 2014, 27(6): 1351-1366.

DOI：10.1088/0951-7715/27/6/1351

• normal hyperbolicity
• geometric singular perturbation theory
• unbounded slow manifolds
• blow-up method

This work is motivated by mathematical questions arising in differential equation models for autocatalytic reactions. We extend the local theory of singularities in fast-slow polynomial vector fields to classes of unbounded manifolds which lose normal hyperbolicity due to an alignment of the tangent and normal bundles. A projective transformation is used to localize the unbounded problem. Then the blow-up method is employed to characterize the loss of normal hyperbolicity for the transformed slow manifolds. Our analysis yields a rigorous scaling law for all unbounded manifolds which exhibit a power- lawdecay for the alignment with a fast subsystem domain. Furthermore, the proof also provides a technical extension of the blow- up method itself by augmenting the analysis with an optimality criterion for the blow- up exponents.

• 出版日期2014-6