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25 lines
620 B
Markdown
25 lines
620 B
Markdown
---
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id: 20250911170650
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title: Lipschitz Continuous
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type: permanent
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created: 2025-09-11T21:06:50Z
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modified: 2025-09-16T16:32:37Z
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tags: []
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---
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# Lipschitz Continuous
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Lipschitz continuous functions are a special case of
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continuous functions. Lipschitz continuity means that a cone
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can be created with slope less than some real number
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$K$.
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Fora a real valued function in one dimension, Lipschitz
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continuity is defined as:
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$$| f(x_1) - f(x_2)| \leq K|x_1 - x_2|$$
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Lipschitz continuity can be expanded to vector fields. From
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here, we can say that ODE trajectories do NOT intersect, and
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that every trajectory is unique.
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