Consider the decimal shift map on the unit interval given by x n+1 =10x n (mod1) . a) The graph of the map is to be drawn. b) Find all fixed points. c) Prove that the map has periodic points of all periods, but all of them are unstable. d) Prove that the map has infinitely many aperiodic orbits. e) Show that the map has sensitive dependance on initial conditions by considering the rate of separation of two nearby orbits. Concept Introduction: ➢ The logistic map is a second-degree equivalent mapping. It has mention how its complex points and the chaotic logistic map is used to arise into a very straightforward non-linear dynamic equation. ➢ The logistic map function is x n+1 = f(x n ) .

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Do College Students With Part-Time Jobs Sleep Less? College students were surveyed about the number of hours they sleep each night.Group A = With part-time jobs | Group B = Without jobs Group A: 6, 5, 7, 6, 5Group B: 8, 7, 9, 8, 7 Instructions: State your hypothesis and perform a two-sample t-test with all formulas. Create histograms for each group. Label axes and add titles. Comment on the distribution shape (e.g., normal, skewed, etc.).Solve on pen and paper

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Question

Chapter 10.3, Problem 7E

Interpretation Introduction

Interpretation:

Consider the decimal shift map on the unit interval given by xn+1=10xn(mod1).

a) The graph of the map is to be drawn.

b) Find all fixed points.

c) Prove that the map has periodic points of all periods, but all of them are unstable.

d) Prove that the map has infinitely many aperiodic orbits.

e) Show that the map has sensitive dependance on initial conditions by considering the rate of separation of two nearby orbits.

Concept Introduction:

➢ The logistic map is a second-degree equivalent mapping. It has mention how its complex points and the chaotic logistic map is used to arise into a very straightforward non-linear dynamic equation.

➢ The logistic map function is xn+1= f(xn).

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