The stable manifold theorem via an isolating block

1973 ◽  
pp. 135-144 ◽  
Author(s):  
Richard McGehee
Keyword(s):  
Stable Manifold ◽  
Isolating Block ◽  
Stable Manifold Theorem

Local stable manifold theorem for fractional systems

2015 ◽  
Vol 83 (4) ◽  
pp. 2435-2452 ◽  
Author(s):  
Amey Deshpande ◽  
Varsha Daftardar-Gejji
Keyword(s):  
Stable Manifold ◽  
Fractional Systems ◽  
Stable Manifold Theorem ◽  
Local Stable Manifold

scholarly journals Integrability of continuous bundles

2019 ◽  
Vol 2019 (752) ◽  
pp. 229-264 ◽  
Author(s):  
Stefano Luzzatto ◽  
Sina Tureli ◽  
Khadim War
Keyword(s):  
Dynamical Systems ◽  
Stable Manifold ◽  
Arbitrary Dimension ◽  
Sufficient Conditions ◽  
Classical Theorem ◽  
Uniqueness Of Solutions ◽  
Stable Manifold Theorem ◽  
New Criteria

Abstract We give new sufficient conditions for the integrability and unique integrability of continuous tangent subbundles on manifolds of arbitrary dimension, generalizing Frobenius’ classical theorem for {C^{1}} subbundles. Using these conditions, we derive new criteria for uniqueness of solutions to ODEs and PDEs and for the integrability of invariant bundles in dynamical systems. In particular, we give a novel proof of the Stable Manifold Theorem and prove some integrability results for dynamically defined dominated splittings.

scholarly journals Erratum to: Local stable manifold theorem for fractional systems

2017 ◽  
Vol 87 (4) ◽  
pp. 2779-2780 ◽  
Author(s):  
Amey Deshpande ◽  
Varsha Daftardar-Gejji
Keyword(s):  
Stable Manifold ◽  
Fractional Systems ◽  
Stable Manifold Theorem ◽  
Local Stable Manifold
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