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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Hausdorff dimension, singular vectors and divergent trajectories
豪斯多夫维数 奇异向量 发散轨迹
2023/5/12
In this talk, I will give a survey of results related to the problem of computing Hausdorff dimension of various dynamically defined sets, such as singular vectors. The aim is to try to describe the l...
We consider the evolution of a connected set in Euclidean space
carried by a periodic incompressible stochastic
ow. While for almost every
realization of the random
ow at time t most of the part...
An Example of a Nearly Integrable Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension
Nearly Integrable Hamiltonian System Trajectory Dense Maximal Hausdorff Dimension
2015/9/25
The famous ergodic hypothesis suggests that for a typical Hamiltonian on a typical energy surface nearly all trajectories are dense. KAM theory disproves it.Ehrenfest (The Conceptual Foundations of th...
On Hausdorff dimension of oscillatory motions in three body problems
Hausdorff dimension oscillatory motions three body problems
2015/9/25
We show that for the Sitnikov example and for the restricted planar circular 3–body problem the set of oscillatory motions often has maximal Hausdorff dimension. Also, we construct Newhouse domains fo...
Comment on “Hausdorff Dimension of Critical Fluctuations in Abelian Gauge Theories”
Comments letter reply
2014/12/20
A Comment on the Letter by J. Hove, S. Mo, and A. Sudbø Phys. Rev. Lett. 85, 2368 (2000). The authors of the Letter offer a Reply.
Measures of the full Hausdorff dimension for a general Sierpinski carpet
Sofic measure Sierpinski carpet matrix-valued potential Gibbs measure a-weighted thermodynamic formalism
2012/6/21
The measure of the full dimension for a general Sierpi\'{n}ski carpet is studied. In the first part of this study, we give a criterion for the measure of the full Hausdorff dimension of a Sierpi\'{n}s...
The conformal loop ensemble CLE_kappa is the canonical conformally invariant probability measure on non-crossing loops in a proper simply connected domain in the complex plane. The parameter kappa var...
From almost sure local regularity to almost sure Hausdorff dimension for Gaussian fields
Gaussian processes Hausdorff dimension (multi)fractional Brownian motion multiparameter processes Holder regularity stationarity
2012/6/19
Fine regularity of stochastic processes is usually measured in a local way by local H\"older exponents and in a global way by fractal dimensions. Following a previous work of Adler, we connect these t...
Exponential growth of norms in semigroups of linear automorphisms and Hausdorff dimension of self-projective IFS
Exponential growth of norms semigroups of linear automorphisms Hausdorff dimension self-projective IFS Dynamical Systems
2012/4/17
Given a finitely generated semigroup S of the (normed) set of linear maps of a vector space V into itself, we find sufficient conditions for the exponential growth of the number N(k) of elements of th...
Hausdorff dimension of visibility sets for well-behaved continuum percolation in the hyperbolic plane
Boolean model continuum percolation fractal geometry Hausdorff-dimension hyperbolic geometry
2011/7/27
Abstract: Let Z be a so-called well-behaved percolation, i.e. a certain random closed set in the hyperbolic plane, whose law is invariant under all isometries; for example the covered region in a Pois...
Hausdorff dimension of a particle path in a quantum manifold
Hausdorff dimension quantum manifold
2010/10/27
After recalling the concept of Hausdorff dimension, we study the fractal properties of a quantum particle path. As a novelty we consider the possibility for the space where the particle propagates, to...
Geometric renormalisation and Hausdorff dimension for loop-approximable geodesics escaping to infinity
Kleinian groups Poincar´ e exponent fractal geometry dissipative dy-namics
2010/11/29
The main result of this paper is to show that if N is a normal subgroup of a Kleinian group G such that G/N contains a coset which is represented by some loxodromic element, then the Hausdorff dimensi...
HAUSDORFF DIMENSION OF CUTSET OF COMPLEX VALUED RADEMACHER SERIES
Hausdorff dimension fractals
2007/12/11
Cutsets of series form an important class of fractal sets. In this paper, the author obtains the Hausdoff dimension of outset of complex valued Rademacher serise.