Smale flows on S2×S1\mathbb{S}^2\times\mathbb{S}^1

In this paper, we use abstract Lyapunov graphs as a combinatorial tool to obtain a complete classification of Smale flows on $\mathbb{S}^2\times\mathbb{S}^1$. This classification gives necessary and sufficient conditions that must be satisfied by an abstract Lyapunov graph in order for it to be associated to a Smale flow on $\mathbb{S}^2\times\mathbb{S}^1$

Are Public Banks pro-Competitive? Evidence from Concentrated Local Markets in Brazil

We measure the competitive effect of public ownership of banks in concentrated local banking markets in Brazil by extending Bresnahan and Reiss’s [1991] framework to measure the effects of entry in concentrated markets. We use variation in market size, the number of competitors and their identity to infer how conduct is affected by the entry of a private vis-à-vis a public bank. We find that, while local markets whose structure is private bank duopoly are 100% larger than private monopolies, duopolies with one public and one private bank and private monopolies are no different with respect to market size. These results suggest that, while the presence of private banks toughens competition, public banks do not affect conduct.banking industry; public versus private ownership; effect of entry.

Conley theory for Gutierrez-Sotomayor fields

In [6], a characterization and genericity theorem for C^1-structurally stable vector fields tangent to a 2-dimensional compact subset M of R^k are established. Also in [6], new types of structurally stable singularities and periodic orbits are presented. In this work we study the continuous flows associated to these vector fields, which we refer to as the Gutierrez-Sotomayor flows on manifolds M with simple singularities, GS flows, by using Conley Index Theory. The Conley indices of all simple singularities are computed and an Euler characteristic formula is obtained. By considering a stratification of M which decomposes it into a union of its regular and singular strata, certain Euler type formulas which relate the topology of M and the dynamics on the strata are obtained. The existence of a Lyapunov function for GS flows without periodic orbits and singular cycles is established. Using long exact sequence analysis of index pairs we determine necessary and sufficient conditions for a GS flow to be defined on an isolating block. We organize this information combinatorially with the aid of Lyapunov graphs and using a Poincaré-Hopf equality we construct isolating blocks for all simple singularities22241277CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQFUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP305649/2018-32018/13481-015th International Workshop on Real and Complex Singularities2020São Carlos, SPUniversidade de São Paul