Abstract We consider partially hyperbolic diffeomorphisms on compact manifolds. define the notion of unstable and stable foliations stably carrying some unique non-trivial homologies. Under this topological assumption, we prove following two results: if center foliation is one-dimensional, then entropy locally a constant; two-dimensional, continuous set all $C^{\infty }$ diffeomorphisms. The proof uses invariant introduced, Yomdin’s theorem upper semi-continuity, Katok’s lower...

We show that, for any <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Superscript 1"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:annotation encoding="application/x-tex">C^1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> partially hyperbolic diffeomorphism, there is a full volume subset such that Cesàro limit of point in this satisfies the Pesin formula partial...

In this paper, we give some necessary conditions for the existence of positive solutions integral systems.

Abstract A localized triangular differential quadrature method is introduced in this article. Not only the existing limitation on approximation order eliminated but also convergent rate enhanced new method. As an example to validate method, elastic torsion of prismatic shaft with regular polygonal cross section studied and excellent agreement available theoretical analytic solutions reached. It believed that present work further widens applicability technique. © 2003 Wiley Periodicals, Inc....

We show that for any $C^1$ partially hyperbolic diffeomorphism, there is a full volume subset, such Cesaro limit of point in this subset satisfies the Pesin formula partial entropy. This result has several important applications. First we $C^{1+}$ diffeomorphism with one dimensional center, every set belongs to either basin physical measure non-vanishing center exponent, or exponent sequence $\frac1n\sum_{i=0}^{n-1}δ_{f^i(x)}$ vanishing. also prove mostly contracting it admits neighborhood...

We consider partially hyperbolic diffeomorphisms on compact manifolds where the unstable and stable foliations stably carry some unique non-trivial homologies. prove following two results: if center foliation is one dimensional, then topological entropy locally a constant; continuous set of all $C^\8$ diffeomorphisms. The proof uses invariant we introduced; Yomdin's theorem upper semi-continuity; Katok's lower semi-continuity for dimensional systems refined Pesin-Ruelle inequality proved

We study entropies caused by the unstable part of partially hyperbolic systems. define metric entropy and topological entropy, establish a variational principle for diffeomorphsims, which states that is supremum taken over all invariant measures. The an measure defined as conditional along manifolds, it turns out to be same given Ledrappier-Young, though we do not use increasing partitions. equivalently via separated sets, spanning sets open covers piece leaf, coincides with volume growth...