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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Expanding cone and homogeneous dynamics
膨胀锥体 均匀动力学 非紧致简单李群
2023/3/18
We introduce the notion of expanding cone of a noncompact simple Lie group. This allows us to extend several results in homogeneous dynamics to more general settings. We show how this notion is used i...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Birkhoff genericity for points on curves in expanding horospheres and Diophantine applications
星座图 曲线 Birkhoff泛型 丢番图应用
2022/11/10
Let $\{a(t):t \in \mathbb{R}\}$ be a diagonalizable subgroup of $SL(d,\mathbb{R})$ for which the expanded horosphere $U$ is abelian. By the Birkhoff ergodic theorem, for any point $x \in SL(d,\mathbb{...
THE DIFFUSION COEFFICIENT FOR PIECEWISE EXPANDING MAPS OF THE INTERVAL WITH METASTABLE STATES
DIFFUSION COEFFICIENT WITH METASTABLE STATES
2015/9/29
Consider a piecewise smooth expanding map of the interval possessing several
invariant subintervals and the same number of ergodic absolutely continuous invariant probability measures (ACIMs).
REGULARITY OF ABSOLUTELY CONTINUOUS INVARIANT MEASURES FOR PIECEWISE EXPANDING UNIMODAL MAPS
INVARIANT MEASURES UNIMODAL MAPS
2015/9/29
An important discovery of the 20th century mathematics is that many deterministic
systems exhibit stochastic behavior. The stochasticity is caused by exponential divergence of nearby trajectories. Th...
An Alternative Approach to Generalised BV and the Application to Expanding Interval Maps
Generalised bounded variation transfer operator expanding map spectral gap
2012/6/6
We introduce a family of Banach spaces of measures, each containing the set of measures with density of bounded variation. These spaces are suitable for the study of weighted transfer operators of pie...
Expanding Semiflows on Branched Surfaces and One-Parameter Semigroups of Operators
Expanding Semiflows Branched Surfaces One-Parameter Semigroups of Operators Dynamical Systems
2012/6/6
We consider expanding semiflows on branched surfaces. The family of transfer operators associated to the semiflow is a one-parameter semigroup of operators. The transfer operators may also be viewed a...
The number of integer points in a family of anisotropically expanding domains
number of integer points family of anisotropically expanding domains Number Theory
2012/4/1
We investigate the remainder in the asymptotic formula for the number of integer points in a family of bounded domains in the Euclidean space, which remain unchanged along some linear subspace and exp...
On stochastic stability of non-uniformly expanding interval maps
stochastic stability non-uniformly expanding interval maps Dynamical Systems
2011/7/13
Abstract: We study the expanding properties of random perturbations of regular interval maps satisfying the summability condition of exponent one. Under mild conditions, we prove strong stochastic sta...
Axi-symmetric deformation due to expanding surface loads in a fluid saturated porous medium
Ring load disc load pore pressure
2010/12/30
The general solution to the field equations of fluid saturated incompressible porous medium for two dimensional axi-symmetric problem is obtained due to time harmonic ring and disc loads by applying H...
In previous work, a class of noninvertible topological dynamical systems $f: X \to X$ was introduced and studied; we called these {\em topologically coarse expanding conformal} systems. To such a sys...
We study the dynamics of Thurston maps under iteration.These are branched covering maps f of 2-spheres S2 with a finite set post(f) of postcritical points.
Spectral triples and Gibbs measures for expanding maps on Cantor sets
spectral triple Dixmier trace expanding map Gibbs measure
2010/9/1
Let T : ! be an expanding map on a Cantor set. For each suitably normalized H¨older continuous potential, we construct a spectral triple from which one may recover the associated Gibbs measure as ...
Statistical properties of nonuniformly expanding 1d maps with logarithmic singularities
Statistical properties of nonuniformly 1d maps logarithmic singularities
2010/9/1
For a certain parametrized family of maps on the circle, with critical points and
logarithmic singularities where derivatives blow up to infinity, a positive measure set of parameters was constructed...