Suppose we have a piecewise function
f(t) = exp(c*t) when 0 <= t < 2 and f(t) = 0 when t >= 2.
Can the above be rewritten as
f(t)= exp(at)*[H(t-0) - H(t-2)],
H is a heaviside function.
THanks for the reply I will try it out.
EDIT: It works now. However, out of self-interest I would like to understand a bit more abour your statement. Isnt |h(x)| = -h(x) when x < 0? In this case x <= 1/2, so how would it be true that |h(x)| = -h(x) (when the condition is when its x < 0?
Selig
I used the affine transform you provdd ie. 2x-1 and it did not yield a conjugation. my work:
g(h(x)) = 1-2|2x-1|
h(T(x)) =
x <= 1/2: 2(2x) - 1 = 4x - 1 \neq -4x+3 = 1-2(2x-1) = g(h(x))
x >= 1/2: 2(2-2x) - 1 = 4 - 4x - 1 = -4x + 3 = 1-2(2x-1) = 1-4x + 3 = -4x + 3 = g(h(x))
this is of...
Thanks for the reply. Good point on the cosine being even - Forgot about that. I tried your "straightforward" approach, however no luok so far. If I'm not mistaken the homeomoprhism has to be algebraic at this point. I don't see a way of simplifying trig functions with those | | being part of...
Find a topological conjugation between g(x) and T(x) where g and T are mappings (both tent maps [graphically speaking])
g:[-1, 1] → [-1,1]
g(x) = 1-2|x|
T:[0,1] → [0, 1]
T(x) = 2x when x ≤ 1/2 and 2(1-x) when x ≥ 1/2
h ° T = g ° h (homeomorphism)
h:[0, 1] → [-1, 1]
h(x) = cos(∏x)...
Homework Statement
Find a topological conjugation between g(x) and T(x) where g and T are mappings (both tent maps [graphically speaking])
Homework Equationsg:[-1, 1] → [-1,1]
g(x) = 1-2|x|
T:[0,1] → [0, 1]
T(x) = 2x when x ≤ 1/2 and 2(1-x) when x ≥ 1/2
h ° T = g ° h (homeomorphism)The...
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