A Piecewise-Linear Fixed Point Theorem.
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| Title: | A Piecewise-Linear Fixed Point Theorem. |
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| Authors: | Simpson, David J.W. (AUTHOR) d.j.w.simpson@massey.ac.nz |
| Source: | American Mathematical Monthly. Aug/Sep2025, Vol. 132 Issue 7, p695-699. 5p. |
| Subject Terms: | Bifurcation theory, Fixed point theory, Stability theory, Dynamical systems, Mathematical functions, Continuous functions, Linear algebra |
| Abstract: | We prove that if a continuous piecewise-smooth map on R n is comprised of two linear functions, has a bounded orbit, and satisfies a certain non-degeneracy condition, then it has a fixed point. The result has important consequences to the bifurcation theory of nonsmooth dynamical systems, yet the proof requires only elementary linear algebra. [ABSTRACT FROM AUTHOR] |
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| Database: | Education Research Complete |
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