GUTIERREZ{SOTOMAYOR FLOWS ON SINGULAR SURFACES

Author(s)

De Rezende, Ketty A. ; Grulha, Nivaldo G., Jr. ; Lima, Dahisy V. S. ; Zigart, Murilo A. J.

• Document type: Journal article
• Source: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS; v. 60, n. 1, p. 45-pg., 2022-09-01.

Abstract

In this work, we consider the collection of necessary homological conditions previously obtained via Conley index theory for a Lyapunov semi-graph to be associated to a Gutierrez-Sotomayor flow on an isolating block and address their sufficiency. These singular flows include regular R, cone C, Whitney W, double D and triple T crossing singularities. Local sufficiency of these conditions are proved in the case of Lyapunov semigraphs along with a complete characterization of the branched 1-manifolds that make up the boundary of the block. As a consequence, global sufficient conditions are determined for Lyapunov graphs labelled with R, C, W, D and T and with minimal weights to be associated to Gutierrez-Sotomayor flows on closed singular 2-manifolds. By removing the minimality condition, we prove other global realizability results by requiring that the Lyapunov graph be labelled with R, C and W singularities or that it be linear. (AU)

• FAPESP's process: 19/21181-0 - New frontiers in Singularity Theory
• Grantee: Regilene Delazari dos Santos Oliveira
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 20/11326-8 - An algebraic-topological approach to dynamical systems and symplectic topology
• Grantee: Dahisy Valadão de Souza Lima
• Support Opportunities: Regular Research Grants
• FAPESP's process: 18/13481-0 - Geometry of control, dynamical and stochastic systems
• Grantee: Marco Antônio Teixeira
• Support Opportunities: Research Projects - Thematic Grants