Transversality theorems on generic linearly perturbed mappings
Shunsuke Ichiki
TL;DR
This paper extends Mather's transversality results by establishing two new theorems on generic linearly perturbed mappings, with applications demonstrating their utility in differential topology.
Contribution
It introduces two novel transversality theorems for generic linearly perturbed $C^r$ mappings, expanding the scope of Mather's original work.
Findings
Two transversality theorems for linearly perturbed mappings
Applications illustrating the theorems' usefulness
Extension of Mather's projections results
Abstract
In his celebrated paper "Generic projections", John Mather has given a striking transversality theorem and its applications on generic projections. On the other hand, in this paper, two transversality theorems on generic linearly perturbed mappings are shown . Moreover, some applications of the two theorems are also given.
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Taxonomy
TopicsDifferential Equations and Numerical Methods · Nonlinear Differential Equations Analysis · Advanced Differential Equations and Dynamical Systems