Timeline for Iteration of a nonlinear map
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Apr 17, 2011 at 18:09 | comment | added | Robert Israel | The general theory (and in particular the Hartman-Grobman theorem, as mentioned by Pietro) can tell you about what happens in a neighbourhood of 0. So if $T$ has $k$ eigenvalues (counted by algebraic multiplicity) with absolute value $< 1$ and none with absolute value $=1$, there will be a $k$-dimensional manifold near 0 on which the iterates will converge to 0. If there are fixed points other than 0, the linearizations around those fixed points will tell you about convergence to them. | |
| Apr 17, 2011 at 16:04 | comment | added | silkrain | The nonlinear map $S$ that I am interested in is equal to a linear map $T$ plus a polynomial in $x$. I want to know for what kind of $x$ $S^kx$ will converge as $k$ grows and where it will converge to. | |
| Apr 17, 2011 at 8:28 | history | answered | Robert Israel | CC BY-SA 3.0 |