Blogs about: Hausdorff Dimension

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Homoclinic/heteroclinic bifurcations: slightly fat horseshoes B

matheuscmss wrote 7 months ago: In what follows, we will consider the same setting of the previous post, and we will discuss a recen … more →

Tags: mathematics, math.DS, Expository, Jean-Christophe Yoccoz, Jacob Palis, Non-uniformly hyperbolic horseshoes, stable sets

Homoclinic/heteroclinic bifurcations: thin horseshoes

matheuscmss wrote 8 months ago: Let be a -diffeomorphism of a surface with a horseshoe and a periodic point whose stable and unstabl … more →

Tags: mathematics, math.DS, Expository, regular Cantor sets, Jacob Palis, Homoclinic bifurcations, Sheldon Newhouse, Floris Takens, thin horseshoes

"Full dimensional sets without given patterns" by Péter Maga

Leonid wrote 10 months ago: The footnote says that the paper is a part of the authors’ Master’s thesis at Eötvös Lor … more →

Tags: Review, pattern avoidance

Congratulations Dr. Demers1 comment

dangillis wrote 1 year ago: There’s a new doctor in the house. He goes by the name of Matt Demers, and today I was privile … more →

Tags: Fractal, Research, Teaching, graduate student, PhD, Presentation, Math, Fixed point (mathematics), Chaos and Fractals

Ultrametrics and the nonlinear Dvoretzky problem5 comments

777 wrote 1 year ago: Hi guys~ The school year here at Princeton is finally (gradually) starting. So I’m back to thi … more →

Tags: bi-lipschitz function, Metric Geometry, Metric, isoperimetric inequality, Assaf Noar, Ultrametric, Terrence Tao

Conférence internationale Géométrie Ergodique (Orsay 2011) III

matheuscmss wrote 1 year ago: For my third post related to the “Conférence Internationale Géométrie Ergodique” (held a … more →

Tags: mathematics, math.DS, math.NT, Expository, Conferences, Conference Geometrie Ergodique, Dmitry Kleinbock, Schmidt games, Diophantine approximation

A remark on a mini-course by Kleiner in Sullivan's 70th birthday2 comments

777 wrote 1 year ago: I spent the last week on Long Island for Dennis Sullivan’s birthday conference. The conference … more →

Tags: hyperbolicity, 3-manifolds, CONFORMAL, Metric Geometry, bruce kleiner, Gromov boundary, Sullivan, groups, Loewner

Chiều Hausdorff và năng lượng Bessel–Riesz

Tuan Minh wrote 2 years ago: Chiều Haudorff của một tập được định nghĩa là infimum của tập các giá trị d không âm sao cho độ đo H … more →

Tags: Probability Theory, Real Analysis, Bessel–Riesz energy, CAPACITY

Coding Fractals by trees

777 wrote 2 years ago: Recently I’ve been editing a set of notes taken by professor Kra during Furstenberg’s co … more →

Tags: Dynamical systems, Ergodic, Fractal, Fürstenberg

Fractals

scienceoftruth wrote 2 years ago: A fractal is “a rough or fragmented geometric shape that can be split into parts, each of whic … more →

Tags: Science, Benoît Mandelbrot, Fractal, selfsimilarity, Karl Weierstrass, Georg Cantor, Felix Hausdorff, Math

Father of Fractals Passes Away

sushant wrote 2 years ago: When a man dies and his obituaries mention the discovery of geometric shapes with a Hausdorff dimens … more →

Tags: Science Facts, Fractal

Hausdorff dimension of projections

777 wrote 3 years ago: A few days ago, professor Wilkinson asked me the following question on google talk (while I was in T … more →

Tags: Amie Wilkinson, Fractal, Projection, foliation, absolute continuous

Kaufman's construction

777 wrote 3 years ago: This is a note on R. Kaufman’s paper An exceptional set for Hausdorff dimension We construct a … more →

Tags: Ergodic, Fractal, kakeya, Fürstenberg

Lower bounds for Hausdorff dimension

jbuzzi wrote 3 years ago: A classical theorem (Marstrand 1954) asserts that, given any Borel subset , the obvious inequality o … more →

Tags: Dynamics, News, Papers, ergodic theory, Entropy

Mathematicians as video game villains, Part 1: Hausdorff3 comments

Matthew Bond wrote 3 years ago: Hausdorff Story: Felix Hausdorff has always lusted for power. No source of knowledge has ever been t … more →

Tags: hausdorff, hausdorff measure, mathematicians as video game villains, separation axioms, T2

245C, Notes 5: Hausdorff dimension (optional)26 comments

Terence Tao wrote 4 years ago: A fundamental characteristic of many mathematical spaces (e.g. vector spaces, metric spaces, topolog … more →

Tags: 245C - Real analysis, math.CA, math.MG, Frostman measure, geometric measure theory, Minkowski dimension

Kakeya Sets in R^22 comments

Matthew Bond wrote 4 years ago: Kakeya sets: Unit Length Line Segments In Every Direction In The x-y Plane Cleverly Arranged To Take … more →

Tags: Besicovitch projection theorem, buffon needle probability, buffon's needle, geometric measure theory, hausdorff measure, Kakeya sets, Level 2 Content


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