Compact integral manifolds of differential systems

TL;DR

This paper establishes boundedness tests for the number of compact integral manifolds across various types of differential systems, providing a unified approach to understanding their solutions.

Contribution

It introduces new boundedness criteria applicable to multiple classes of differential systems, extending previous results to a broader context.

Findings

Proved boundedness tests for autonomous ODE systems

Extended boundedness criteria to partial differential systems

Unified approach for different differential system types

Abstract

The boundedness tests for the number of compact integral manifolds of autonomous ordinary differential systems, of autonomous total differential systems, of linear systems of partial differential equations, of Pfaff systems of equations, and of systems of exterior differential equations are proved.