I'm looking for an example of a dynamical system which is both (measure-theoretically) strongly mixing and uniquely ergodic. I've looked around and found lots of discussion of systems which are uniquely ergodic but not strongly mixing, but which doesn't seem to think there's any tension between the properties, so I suspect there's an easy answer I just don't know.
2026-03-26 08:14:30.1774512870
Strongly mixing uniquely ergodic dynamical system
397 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in DYNAMICAL-SYSTEMS
- Stability of system of parameters $\kappa, \lambda$ when there is a zero eigenvalue
- Stability of stationary point $O(0,0)$ when eigenvalues are zero
- Determine $ \ a_{\max} \ $ and $ \ a_{\min} \ $ so that the above difference equation is well-defined.
- Question on designing a state observer for discrete time system
- How to analyze a dynamical system when $t\to\infty?$
- The system $x' = h(y), \space y' = ay + g(x)$ has no periodic solutions
- Existence of unique limit cycle for $r'=r(μ-r^2), \space θ' = ρ(r^2)$
- Including a time delay term for a differential equation
- Doubts in proof of topologically transitive + dense periodic points = Devaney Chaotic
- Condition for symmetric part of $A$ for $\|x(t)\|$ monotonically decreasing ($\dot{x} = Ax(t)$)
Related Questions in EXAMPLES-COUNTEREXAMPLES
- A congruence with the Euler's totient function and sum of divisors function
- Seeking an example of Schwartz function $f$ such that $ \int_{\bf R}\left|\frac{f(x-y)}{y}\right|\ dy=\infty$
- Inner Product Uniqueness
- Metric on a linear space is induced by norm if and only if the metric is homogeneous and translation invariant
- Why do I need boundedness for a a closed subset of $\mathbb{R}$ to have a maximum?
- A congruence with the Euler's totient function and number of divisors function
- Analysis Counterexamples
- A congruence involving Mersenne numbers
- If $\|\ f \|\ = \max_{|x|=1} |f(x)|$ then is $\|\ f \|\ \|\ f^{-1}\|\ = 1$ for all $f\in \mathcal{L}(\mathbb{R}^m,\mathbb{R}^n)$?
- Unbounded Feasible Region
Related Questions in ERGODIC-THEORY
- the mathematics of stirring
- Kac Lemma for Ergodic Stationary Process
- Ergodicity of a skew product
- Is every dynamical system approaching independence isomorphic to a Bernoulli system?
- Infinite dimensional analysis
- Poincaré's Recurrence Theorem
- Chain recurrent set is the set of fixed points?
- Is this chaotic map known?
- A complex root of unity and "dense" property of the its orbit on the unit circle
- Books on ergodic operators
Related Questions in MIXING
- Mixing time of a random walk
- Ergodic system counterexample
- Density limits and sets with positive lower density
- Mixing time of personalized PageRank random walk
- How to get conditional from mixed normals (Bayes rule)?
- Downsizing baby formula
- Overview of the different types of mixing sequences
- Expressing a CDF with positive support as a mixture of two components
- Is the infinitely distributed lag process strong mixing?
- Is linear combination of strong mixing process still strong mixing?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- 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?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- 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
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Not sure whether you mean topologically or measure theoretically strongly mixing. In the first case the following paper might provide the example you are looking for: http://www.ams.org/journals/tran/1970-148-02/S0002-9947-1970-0259884-8/
but probably your question is about measure theoretic strong mixing and there usually you get many ergodic measures (as most of such systems have periodic points).