The abstract framework in this section was introduced in Hale . Hale and Lopes  (see also Hale , Massatt [32, 33]) proved the result in Section 1 that a compact dissipative α-contraction Tf(t) has A(f) compact, Billotti and LaSalle  proved the same result for point dissipative maps Tf(t) which are completely continuous for t ≥ r. For some other evolutionary systems which are special cases of the abstract framework in Section 1, see Hale , Massatt . For partial results on question Q5, see Chernoff and Marsden , Hale and Scheurle .
KeywordsHopf Bifurcation Unstable Manifold Hausdorff Dimension Abstract Framework Bibliographical Note
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