Broadly speaking, I cannot pin down what is meant by Chaos. I understand that (informally) if a dynamical system is highly sensitive to initial input data then this system is said to be chaotic. Eg the famous Lorenz Equations. However, I have come across the following definition from theencyclopediaofmath.org which states "Chaos describes a situation where typical solutions (or orbits) of a differential equation (or typical evolutions of some other model describing deterministic evolution) do not converge to a stationary or periodic function (of time) but continue to exhibit a seemingly unpredictable behaviour." These two broad definitions seem to mean different things. Can anybody clear any of this up?
2026-03-25 19:02:19.1774465339
Two interpretations of Chaos?
59 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in DEFINITION
- How are these definitions of continuous relations equivalent?
- If a set is open, does it mean that every point is an interior point?
- What does $a^b$ mean in the definition of a cartesian closed category?
- $\lim_{n\to \infty}\sum_{j=0}^{[n/2]} \frac{1}{n} f\left( \frac{j}{n}\right)$
- Definition of "Normal topological space"
- How to verify $(a,b) = (c,d) \implies a = c \wedge b = d$ naively
- Why wolfram alpha assumed $ x>0$ as a domain of definition for $x^x $?
- Showing $x = x' \implies f(x) = f(x')$
- Inferior limit when t decreases to 0
- Is Hilbert space a Normed Space or a Inner Product Space? Or it have to be both at the same time?
Related Questions in CHAOS-THEORY
- Chaotic behaviour from iteration process.
- Doubts in proof of topologically transitive + dense periodic points = Devaney Chaotic
- Homeomorphism between Smale set and $\{0,2\} ^{\mathbb{Z}}$
- Making something a control parameter or a variable when analysing a dynamical system
- Lorenz attractor as a position-velocity-acceleration problem
- Do chaos and/or limit cycles always require the existence of an unstable fixed point?
- Is the "sensitive dependence on initial conditions" of chaotic systems referring to the seed, control parameters, or both?
- Logistic map and chaos on a Cantor set
- Moser invariant curves in discrete dynamical systems and how they give stability
- Why do we need folding and a finite domain for chaos?
Related Questions in NONLINEAR-DYNAMICS
- Numerical solution for a two dimensional third order nonlinear differential equation
- How to find the equation for a manifold of a nonlinear dynamical system?
- Can a 2 cycle occur in logistic map for r=4?
- $w =\operatorname{arcsinh}(1+2\operatorname{arcsinh}(1+2^2\operatorname{arcsinh}(1+2^{2^2}\operatorname{arcsinh}(1+\dotsm$
- Intuition behind dense orbits
- How to find out the critical angle of a ball separating the circle?
- Extended class K function properties
- construction of henon map
- Rigorous interpretation of $\lim_{\|x\|\rightarrow\infty}f(x)$
- How to approximate the following equation?
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?