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I think, after reading what´s written above, we must make a distinction between systems that are big and little, like the atmosphere and a single billiard ball. I´s clear that a billiard ball on a table makes a journey that deviates more and more from the path it would have taken hadn´t you give a slightly different direction in velocity. Consider now a ...

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The phase potrait for this physical system describes the oscillation of the particle described above to be a Homoclinic orbit-that is, the particle oscillating between extreme ends of a double well. No, not even close. I assume that your misunderstanding originates from confusing phase space and geometrical space. Suppose, we describe the dynamical ...

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Many dynamical systems involve recursive sequences of simple functions, $f(f(f(...f(x))))$ which are iterated n times to lead to some discrete iteration sequence (a Picard sequence) with often tractable properties. It is possible however, to analytically continue the discrete iteration index n to a continuous non integer one, fractional, infinitesimal, or ...

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Will there be a symbolic sequence for each dimension or will a symbol be assigned to a point $(x,y)$? This depends what you eventually want to do with your symbol sequence, but for typical applications, such as determining the entropy or modelling, you want to assign one symbol to the point. The general reason behind this is that (for a proper ...

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