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Trying to learn math :)


Oct
28
revised Help defining an open cover
I have added more explanation.
Oct
28
comment Help defining an open cover
@HagenvonEitzen the maps $\Phi_i$ will be solutions of an ODE. Such ODE is well defined on $\mathbb R^2$ but I have some an interest on making a distinction for initial conditions in the three of the $A_i$'s.
Oct
28
comment Help defining an open cover
Say, I want $U_0$ be an open set a bit bigger than $A_0$, and so on for the other ones. That has the "same cone shape".
Oct
28
revised Help defining an open cover
edited body
Oct
28
asked Help defining an open cover
Sep
24
awarded  Autobiographer
Sep
24
accepted How many solutions does the equation $2i+j+3k=l$ have in nonnegative integers?
Sep
24
comment How many solutions does the equation $2i+j+3k=l$ have in nonnegative integers?
thanks a lot for this nice answer!
Sep
21
accepted self-adjoint operator without eigenvalues?
Sep
21
asked How many solutions does the equation $2i+j+3k=l$ have in nonnegative integers?
Sep
18
comment critical points, differential equation
To linearise you take derivative, or the so called Jacobian, and then evaluate the equilibrium point $(x,y)=(a,b/a)$. You can try it yourself and then ask if you have problems.
Sep
18
comment critical points, differential equation
there you go then.
Sep
18
answered critical points, differential equation
Sep
18
comment Proving that maximal interval of existence exists and that solution is unque
Is Gronwall's inequality useful? encyclopediaofmath.org/index.php/Gronwall_lemma
Sep
15
revised Stability analysis for a system of two differential equations
added 1 character in body
Sep
15
answered Stability analysis for a system of two differential equations
Sep
12
comment Stability analysis for a system of two differential equations
You need to check the eigenvalues, and eigenvectors (at each equilibrium point), they will give you a local picture near each equilibrium point. Then you might be able to draw global conclusions. Of course everything will depend on the choice of the parameters, so you may have several distinct cases to consider, e.g. all parameters are positive, or all parameters are negative, and so on.
Sep
4
revised self-adjoint operator without eigenvalues?
added 795 characters in body
Sep
4
asked self-adjoint operator without eigenvalues?
Aug
26
comment Every solution of the system is attracted to the center manifold
**tex text is the extension.