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An important approach to establishing stochastic behavior of dynamical systems is based on the study of systems expanding a foliation and of measures having smooth densities along
the leaves of this ...
Fundamental domain of invariant sets and applications
Fundamental domain partial hyperbolicity cocycle transitivity accessibility essential saturation
2012/4/18
Let $X$ be a compact metric space and $f:X\to X$ a homeomorphism on $X$. We construct a fundamental domain for the set with finite peaks for each cocycle induced by $\phi\in C(X,R)$. In particular we ...
Invariant Measures with Bounded Variation Densities for Piecewise Area Preserving Maps
Bounded Variation Piecewise Area Preserving Maps Dynamical Systems
2011/8/30
Abstract: We investigate the properties of absolutely continuous invariant probability measures (ACIPs) for piecewise area preserving maps (PAPs) on $\mathbb{R}^d$. This class of maps unifies piecewis...
Polytopic Invariant Verification and Synthesis for Polynomial Dynamical Systems via Linear Programming
Polytopic Invariant Verification Synthesis for Polynomial Dynamical Systems Linear Programming
2011/1/18
This paper deals with the veri cation and the synthesis of polytopic invariant sets for
polynomial dynamical systems. An invariant set of a dynamical system is a subset of the state
space such that ...
Prime end rotation numbers of invariant separating contunua of annular homeomorphisms
continuum rotation set prime end rotation number Brouwer line
2011/1/18
Let f be a homeomorphism of the closed annulus A isotopic to the identity, and let X IntA be an f-invariant continuum which separates A into two domains, the upper domain U+ and the lower domain U&#...