Tag Archives: foliations

Fubini foiled

An important issue in hyperbolic dynamics is that of absolute continuity. Suppose some neighbourhood of a smooth manifold is foliated by a collection of smooth submanifolds , where is some indexing set. (Here “smooth” may mean , or , or … Continue reading

Posted in ergodic theory, examples, smooth dynamics | Tagged | 8 Comments

The stable manifold theorem

The stable manifold theorem is one of the most important in the theory of non-linear ODEs and dynamical systems. Unfortunately, some of the standard introductory texts (Hirsch–Smale, Perko) either do not give a proof, or do not motivate the proof, … Continue reading

Posted in ODE, smooth dynamics, theorems | Tagged , | 3 Comments