Expansive measures for flows

C-stably Expansive Sets for Flows

Let X be a C1 vector field on a closed C∞ manifold M . We introduce the concept of C1 stable expansivity for compact Xt-invariant set, and use a flow-version of Mane’s results (Lemma II.3 in ”Mane, R. An ergodic closing lemma. Ann. of Math. (2) 116 (1982), no. 3, 503–540”) on uniformly hyperbolic families of periodic linear differential equations in order to get the hyperbolicity for the C1 sta...

Dimension of Measures for Suspension Flows

We consider suspension flows over two-sided subshifts of finite type and establish an explicit formula for the pointwise dimension of an arbitrary measure (in particular the measure is not necessarily ergodic and it may not possess a local product structure). The applications of this formula include the description of the Hausdorff dimension of a given measure in terms of an ergodic decompositi...

Numerical Solution for Heave of Expansive Soils

A numerical solution for heave prediction is developed within the context theories for both saturated and unsaturated soil behaviors. Basically, lowering the potential level of compressing on a saturated layer will cause heaving due to water absorption. This water absorption is in an opposite way, similar to water dissipation as what happens during unloading in consolidation process. However, i...

Invariant Measures for Passive Tracer Dynamics in Ornstein-uhlenbeck Flows

Ergodic Properties of Equilibrium Measures for Smooth Three Dimensional Flows

Let {T t} be a smooth flow with positive speed and positive topological entropy on a compact smooth three dimensional manifold, and let μ be an ergodic measure of maximal entropy. We show that either {T t} is Bernoulli, or {T t} is isomorphic to the product of a Bernoulli flow and a rotational flow. Applications are given to Reeb flows.