Methods in the Qualitative Theory of Dynamical Systems in Astrophysics and Gas Dynamics (Oleg I. Bogoyavlensky)

SIAM Review ◽  
1986 ◽  
Vol 28 (4) ◽  
pp. 592-593
Author(s):  
Nicholas D. Kazarinoff
Keyword(s):  
Dynamical Systems ◽  
Gas Dynamics ◽  
Qualitative Theory

Qualitative theory of non-smooth dynamical systems

2007 ◽  
pp. 47-119 ◽  
Author(s):  
Mario di Bernardo ◽  
Alan R. Champneys ◽  
Christopher J. Budd ◽  
Piotr Kowalczyk
Keyword(s):  
Dynamical Systems ◽  
Qualitative Theory

The Existence and Bifurcation of Peakon and Anti-Peakon to the n-Degree b-Equation

2018 ◽  
Vol 28 (01) ◽  
pp. 1850014 ◽  
Author(s):  
Jiaopeng Yang ◽  
Zongguang Li ◽  
Zhengrong Liu
Keyword(s):  
Dynamical Systems ◽  
Positive Integer ◽  
Wave Speed ◽  
Qualitative Theory ◽  
Bifurcation Method ◽  
Positive Wave

In this paper, we study the existence and bifurcation of peakon and anti-peakon to the [Formula: see text]-degree [Formula: see text]-equation with [Formula: see text] and positive integer [Formula: see text]. Using qualitative theory and bifurcation method of dynamical systems, for positive wave speed we confirm the following properties: (1) When [Formula: see text], the equation has peakon, but no anti-peakon. (2) When [Formula: see text], the equation has not only peakon but also anti-peakon. There is a bifurcation wave speed for peakon and anti-peakon. (3) When [Formula: see text] is even, there exists a maximum wave speed for peakon. (4) When [Formula: see text] is odd, there is no maximum wave speed for peakon.

scholarly journals On an encounter of two men of mathematics in Lima

2020 ◽  
Vol 20 (40) ◽  
pp. 01-07
Author(s):  
Jorge Sotomayor
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Qualitative Theory ◽  
Research Activity ◽  
Random Event ◽  
Local Meaning

This evocative essay focuses on the encounter of two eminent Men of Mathematics: José Tola Pasquel, Peruvian, and Maurício Matos Peixoto, Brazilian, in November of 1961 in Lima. It glimpses into the local meaning and later mathematical consequences of such apparently random event. Here are discussed its implications for the participation of the author in the starting steps of the Qualitative Theory of Differential Equations, earlier name for Dynamical Systems, as a research activity in Brazil.

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