Hénon map

High school (ages 12+)
Mathematics & Numbers

Name:

Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/h-non-map

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the mathematical formulation?Iterative map: $x{n+1} = 1 - axn^2 + yn$, $y{n+1} = bxn$
2. What is the core phenomenon?Exhibits chaotic dynamics and sensitive dependence on initial conditions

Discrete-Time Dynamical System: A system whose state evolves in distinct steps rather than continuously.
Sensitive Dependence on Initial Conditions: The property where small changes in starting conditions lead to vastly different outcomes over time.
Fractal Dimension: A measure of how completely a fractal fills space, often a non-integer value.
Poincaré Section: A technique to visualize the dynamics of a continuous system by sampling its state at regular intervals.