Finite time blowup of generalized Euler ODE in matrix geometry

TL;DR

This paper investigates the finite time blowup phenomena of generalized Euler ODEs in matrix geometry, extending previous results to singular operators and symmetric matrices, and addressing open questions in the field.

Contribution

It extends Sullivan's finite time blowup results from invertible to singular linear operators and provides a complete answer for symmetric initial matrices.

Findings

Finite time blowup occurs for generalized Euler ODEs in matrix geometry.

Extension of blowup results to singular linear operators.

Complete characterization for symmetric initial matrices.

Abstract

In this paper, we study the finite time blowup of the generalized Euler ODE in the matrix geometry. We can extend Sullivan's result which is about the finite time blowup result of initial invertible linear operators to singular linear operators. we can give a complete answer to the question of Sullivan in the case when the initial matrix A is symmetric in the finite dimensional vector space W. Some open questions are proposed in the last part of the paper.