Recent content by peter.a

What is an induced measure? I have seen the formal definition many times i am trying to get a grasp of this concept. Does an induced measure mean that we can view the measure associated with a random variable as some co-ordinate function defined on R? Is it the cdf?

f[x_] := x^2 + c; y = Solve[f'[f[x]] == 1, x, Reals] output: {{x -> ConditionalExpression[Root[-1 + 4 c #1 + 4 #1^3 &, 1], c > -(3/4) || c < -(3/4)]}, {x -> ConditionalExpression[Root[-1 + 4 c #1 + 4 #1^3 &, 2], c < -(3/4)]}, {x -> ConditionalExpression[Root[-1 + 4 c...

the solution for x is an inequality, shouldn't the solution for k then also be an inequality ?

Thanks for clearing that up, because i was getting confused

h[x_] = x^3 +x^2+ k; Solve[h[x] == 0, k] {{k -> -x^2 - x^3}} Reduce[Abs[h'[x]] >= 1, x] Re[x] < -(1/2) || (-(1/2) <= Re[x] <= 1/2 && (Im[x] <= -(1/2) Sqrt[1 - 4 Re[x]^2] || Im[x] >= 1/2 Sqrt[1 - 4 Re[x]^2])) || Re[x] > 1/2 Now i want to express these inequalities in terms of the value of k...

why have you done f[f[u]==u and not f[u]==u? is this because then it also gives the complex solutions?

How can i use the Solve function to find the actual equation for a fixed point? For the function f(x)=ur(1-u)

Yeah it wasn't working for a bit and i double posted as well. In answer to your question i am new to mathematica and am just practising working through different things. I am following what i see in the online tutorials for the most part.

Whoops hit post 2 times!

Thts amazing! I am a bit intimidated by the fact you did in 2 seconds what i have been working on for the better part of an hour. Thanks. can you tell me how i can plot this stored data using ListPlot ? to see what the relationship is between x and the y values

Hi Bill This is exactly what I am stuck on; I have a function as follows defined; f[a_][x_] := x^2 + a; Then i define w[a_] := Take[NestList[f[-1.8], 0, 1000], 100] Similar to what you mentioned in the previous post Now i want to evaluate this for different values of the constant a...

I have a function of two variables f[x_][y_]=x^2+y; d=Take[NestList[f[-2],0,10],-2]; now i want to repeat this process by changing -2 to -1.99, then -1.98 all the way up to 0 and storing values in a table, so i can later make a plot. I can't figure out how to repeat this process.

Could you explain to me how it works, so i can apply it to other functions, when i try and use thje code for a different function f i get errors?

say I have a function f(x)=x^7+k I want to iterate x(n+1)=f(xn), 50 times starting with x0=1 and keep the last 10 values i want to assigh these values to some function''y'' and be able to use y to calculate this iteration for any input constant K. ie say K=0, K=0.5 etc, and then i want to store...

I have already read that and most other content on the web relating to the prokhorov metric.