By the en.wikipedia, for the self-similar sets in a metric space, the self-similar dimension and the Hausdorff dimension are often the same, but not always. Is there a known sufficient-necessary condition for the sets whose [self-similar dimension and Hausdorff dimension are not same]?
2025-07-03 05:23:36.1751520216
When the self-similar dimension and the Hausdorff dimension are different?
165 Views Asked by Kanu Kim https://math.techqa.club/user/kanu-kim/detail AtRelated Questions in FRACTALS
- Relations between the 2-disc operad and fractals?
- Proving that we have $A \subset K$ where $K$ is self-similar
- On a curve every point of which is a point of ramification
- How to avoid overlap in circle fractals?
- Non-empty interior of a Mandelbox
- Is there a rigorous mathematical definition of the Koch curve?
- Definition of Minkowski dimension
- Are there methods to recursively calculate the decimal expansion of real numbers?
- Cantor set and ternary expansions
- Union of two Cantor sets is also a Cantor set
Related Questions in DIMENSION-THEORY-ANALYSIS
- An open covering of the Topologist's sine curve.
- Definition of Minkowski dimension
- Interpreting infinite integer lattice as a manifold of negative dimension
- Codimension of subspaces of a sphere
- Singular points of one-to-one mapping on rectifiable set
- Hausdorff dimension of homeomorphic compact metric spaces
- How to characterize the dimension of a manifold using homology?
- Continuous one-to-one mapping from a subset $K \subset \mathbb{R}^n$ of positive measure to $\mathbb{R}^{n-1}$
- Lipschitz continuous one-to-one mapping from subset $K\subset\mathbb{R}^n$ of positive measure to $\mathbb{R}^{n-1}$
- Showing an equation satisfies laplace equation
Related Questions in HAUSDORFF-MEASURE
- How prove that $m_\alpha ^*(\mathcal C)\geq 1$ where $\mathcal C$ is the Cantor set, and $m_\alpha $ the Hausdorff measure.
- Compute Hausdorff dimension of cantor set.
- What are the sufficient conditions for a function to take a Hausdorff space to another Hausdorff space.
- About the Moment of Inertia of the Cantor Set
- Show that for all $\varepsilon>0$ there is a compact $K\subset E$ s.t. $m_\alpha (E\backslash K)<\varepsilon$.
- Exact value of Hausdorff measure of middle-third Cantor set
- Prove that that a map in $C^N$ in the metric topology is continuous to the Zariski topology, but that the map is not a homeomorphism.
- Does there exist a curve with non zero area?
- Hausdorff distance on power sets
- Hausdorff dimension of a Cantor Set: attaining a lower bound
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Refuting the Anti-Cantor Cranks
- Find $E[XY|Y+Z=1 ]$
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- What are the Implications of having VΩ as a model for a theory?
- How do we know that the number $1$ is not equal to the number $-1$?
- Defining a Galois Field based on primitive element versus polynomial?
- Is computer science a branch of mathematics?
- Can't find the relationship between two columns of numbers. Please Help
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent
- Alternative way of expressing a quantied statement with "Some"
Popular # Hahtags
real-analysis
calculus
linear-algebra
probability
abstract-algebra
integration
sequences-and-series
combinatorics
general-topology
matrices
functional-analysis
complex-analysis
geometry
group-theory
algebra-precalculus
probability-theory
ordinary-differential-equations
limits
analysis
number-theory
measure-theory
elementary-number-theory
statistics
multivariable-calculus
functions
derivatives
discrete-mathematics
differential-geometry
inequality
trigonometry
Popular Questions
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- How to find mean and median from histogram
- Difference between "≈", "≃", and "≅"
- Easy way of memorizing values of sine, cosine, and tangent
- How to calculate the intersection of two planes?
- What does "∈" mean?
- If you roll a fair six sided die twice, what's the probability that you get the same number both times?
- Probability of getting exactly 2 heads in 3 coins tossed with order not important?
- Fourier transform for dummies
- Limit of $(1+ x/n)^n$ when $n$ tends to infinity