arXiv subjects

Yongluo Cao

Publications and source records attributed to Yongluo Cao.

27 records · Page 2Linked to original sources

arXiv2012

Nonadditive Measure-theoretic Pressure and Applications to Dimensions of an Ergodic Measure

Without any additional conditions on subadditive potentials, this paper defines subadditive measure-theoretic pressure, and shows that the subadditive measure-theoretic pressure for ergodic measures can be described in terms of measure-theoretic entropy and a constant associated with the ergodic measure. Based on the definition of topological pressure on non-compact set, we give another equivalent definition of subadditive measure-theoretic pressure, and obtain an inverse variational principle. This paper also studies the supadditive measure-theoretic pressure which has similar formalism as the subadditive measure-theoretic pressure. As an application of the main results, we prove that an average conformal repeller admits an ergodic measure of maximal Haudorff dimension. Furthermore, for each ergodic measure supported on an average conformal repeller, we construct a set whose dimension is equal to the dimension of the measure.

math.DS↗

arXiv2010

Pressures for Asymptotically Sub-additive Potentials Under a Mistake Function

This paper defines the pressure for asymptotically subadditive potentials under a mistake function, including the measuretheoretical and the topological versions. Using the advanced techniques of ergodic theory and topological dynamics, we reveals a variational principle for the new defined topological pressure without any additional conditions on the potentials and the compact metric space.

math.DS↗

arXiv2009

On the topological pressure of random bundle transformations in sub-additive case

In this paper, we define the topological pressure for sub-additive potentials via separated sets in random dynamical systems and we give a proof of the relativized variational principle for the topological pressure.

math.DS↗

arXiv2009

The Hausdorff dimension of average conformal repellers under random perturbation

We prove that the Hausdorff dimension of an average conformal repeller is stable under random perturbations. Our perturbation model uses the notion of a bundle random dynamical system.

math.DS↗

arXiv2007

Uniform hyperbolicity for random maps with positive Lyapunov exponents

We consider some general classes of random dynamical systems and show that a priori very weak nonuniform hyperbolicity conditions actually imply uniform hyperbolicity.

math.DS↗

arXiv2007

The boundary of hyperbolicity for Henon-like families

We consider C^{2} Henon-like families of diffeomorphisms of R^{2} and study the boundary of the region of parameter values for which the nonwandering set is uniformly hyperbolic. Assuming sufficient dissipativity, we show that the loss of hyperbolicity is caused by a first homoclinic or heteroclinic tangency and that uniform hyperbolicity estimates hold uniformly in the parameter up to this bifurcation parameter and even, to some extent, at the bifurcation parameter.

math.DS↗

arXiv2004

Some non-hyperbolic systems with strictly non-zero Lyapunov exponents for all invariant measures: Horseshoes with internal tangencies

We study the hyperbolicity of a class of horseshoes exhibiting an internal tangency, i.e. a point of homoclinic tangency accumulated by periodic points. In particular these systems are strictly not uniformly hyperbolic. However we show that all the Lyapunov exponents of all invariant measures are uniformly bounded away from 0. This is the first known example of this kind.

math.DS↗

arXiv2003

A minimum principle for Lyapunov exponents and a higher-dimensional version of a Theorem of Mane'

We consider compact invariant sets Λfor C^{1} maps in arbitrary dimension. We prove that if Λcontains no critical points then there exists an invariant probability measure with a Lyapunov exponent λwhich is the minimum of all Lyapunov exponents for all invariant measures supported on Λ. We apply this result to prove that Λis uniformly expanding if every invariant probability measure supported on Λis hyperbolic repelling. This generalizes a well known theorem of Mane' to the higher-dimensional setting.

math.DS↗

arXiv1998

The isolated saddle-node bifurcation occurring inside a horseshoe

In this paper, we consider a smooth arc of diffeomorphisms which has a saddle-node bifurcation inside a nontrivial invariant set which is a deformation of a horseshoe. We show that this saddle-node bifurcation is isolated, that is, its hyperbolicity is maintained before and after the saddle-node bifurcation. Moreover we construct a $C^2$-open set of arcs having the same property.

math.DS↗