Hyperbolas near an unstable fixed point (FP) are super awesome! For an observer, the phase space cannot look anymore beautiful. They provide no bounds and stretch to infinities on all quadrants. But the poor, untrained physical world loves ellipses. Small, closed objects with limited scope, these ellipses just end up constraining the philosophical output. Yet, the Royal Society has such an elliptic foundation that infinities, although powerful, are yet struggling to find admirers.
A few days ago, the unstable FP was sitting happily in his static position while a particle rolled towards it from the second quadrant. The particle, being close to its minimum, didn't want to move any further. The FP liked the fact that he had someone to meet after a long time. But he has seen many a particle along the same trajectory. They come, they leave. Nature's laws don't change. But unusually, this particle wasn't showing any intention of leaving. The FP knew that someone must have tampered with the action. The FP was now angry. No one messes with his phase space.
The mathematician looked at the screen with a cunning smile on his lips. Watching the changing phase structures with each change of parameters gave him a super-human happiness. He looked at his finger tips. He felt powerful. He peered into the screen. The equations have changed. The point has been tamed. An ellipse has locked it in.
A few days ago, the unstable FP was sitting happily in his static position while a particle rolled towards it from the second quadrant. The particle, being close to its minimum, didn't want to move any further. The FP liked the fact that he had someone to meet after a long time. But he has seen many a particle along the same trajectory. They come, they leave. Nature's laws don't change. But unusually, this particle wasn't showing any intention of leaving. The FP knew that someone must have tampered with the action. The FP was now angry. No one messes with his phase space.
The mathematician looked at the screen with a cunning smile on his lips. Watching the changing phase structures with each change of parameters gave him a super-human happiness. He looked at his finger tips. He felt powerful. He peered into the screen. The equations have changed. The point has been tamed. An ellipse has locked it in.
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