Rigorous computations in dynamics

• Grant number: 16/08704-5
• Support Opportunities: Regular Research Grants
• Start date: September 01, 2016
• End date: November 30, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Marcio Fuzeto Gameiro
• Grantee: Marcio Fuzeto Gameiro
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• City of the host institution: São Carlos

Abstract

The goal of this research project is to develop rigorous computer assisted methods to study the dynamics of differential equations. The goal is to extend the so-called rigorous continuation method to prove the existence of periodic solutions, homoclinic and heteroclinic orbits, determine the stability of these orbits and to compute invariant manifolds. (AU)

Scientific publications

(7)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

FIGUERAS, JORDI-LLUIS; GAMEIRO, MARCIO; LESSARD, JEAN-PHILIPPE; DE LA LLAVE, RAFAEL. A Framework for the Numerical Computation and A Posteriori Verification of Invariant Objects of Evolution Equations. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 16, n. 2, p. 1070-1088, 2017. (16/08704-5, 13/50382-7, 10/00875-9, 13/07460-7)

RODRIGUES, HILDEBRANDO M.; CARABALLO, TOMAS; GAMEIRO, MARCIO. DYNAMICS OF A CLASS OF ODES VIA WAVELETS. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v. 16, n. 6, p. 2337-2355, NOV 2017. (13/07460-7, 16/21032-6, 16/08704-5, 15/19165-5)

RODRIGUES, HILDEBRANDO M.; WU, JIANHONG; GAMEIRO, MARCIO. SWITCHING SYNCHRONIZED CHAOTIC SYSTEMS APPLIED TO SECURE COMMUNICATION. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, v. 8, n. 2, p. 413-426, APR 2018. (13/07460-7, 16/08704-5, 16/21032-6, 10/00875-9, 14/12277-0)

GAMEIRO, MARCIO; LESSARD, JEAN-PHILIPPE. A Posteriori Verification of Invariant Objects of Evolution Equations: Periodic Orbits in the Kuramoto-Sivashinsky PDE. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 16, n. 1, p. 687-728, 2017. (10/00875-9, 13/50382-7, 16/08704-5, 13/07460-7)

GAMEIRO, MARCIO; SINGH, ABHINENDRA; KONDIC, LOU; MISCHAIKOW, KONSTANTIN; MORRIS, JEFFREY F.. Interaction network analysis in shear thickening suspensions. PHYSICAL REVIEW FLUIDS, v. 5, n. 3, MAR 23 2020. (16/08704-5, 16/21032-6)

CASTELLI, ROBERTO; GAMEIRO, MARCIO; LESSARD, JEAN-PHILIPPE. Rigorous Numerics for ill-posed PDEs: Periodic Orbits in the Boussinesq Equation. Archive for Rational Mechanics and Analysis, v. 228, n. 1, p. 129-157, APR 2018. (16/08704-5, 16/21032-6, 13/50382-7, 13/07460-7)

RODRIGUES, HILDEBRANDO M.; TEIXEIRA, MARCO A.; GAMEIRO, MARCIO. On Exponential Decay and the Markus-Yamabe Conjecture in Infinite Dimensions with Applications to the Cima System. Journal of Dynamics and Differential Equations, v. 30, n. 3, p. 1199-1219, SEP 2018. (13/07460-7, 16/21032-6, 12/18780-0, 16/08704-5, 15/19165-5)