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I'm starting a project on chaos very soon and I was just wondering...

One of the distinguishing features of a "chaotic system" is the sensitive dependence on initial conditions. It is stated thatifwe knew the initial conditions with infinite precision we would also be able to predict the future behavior of the system, i.e. no chaos. But how? There are no analytical solutions to these problems, so we'd have to rely on numerical integration, which is of course only approximate.

So, suppose we take a point in phase space, which is our infinitely precise initial condition, and start integrating numerically in small timesteps. Because of the sensitive dependence on initial conditions the errors in the numerical integration scheme will amplify greatly and our prediction will be useless... In fact, how can we sayanythingabout these kind of systems without computers of infinite precision?

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# Sensitive dependence on initial conditions

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