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# Effects of dissipation, transient and dynamical properties in discrete mappings

 Grant number: 14/18672-8 Support type: Regular Research Grants Duration: November 01, 2014 - October 31, 2016 Field of knowledge: Physical Sciences and Mathematics - Physics Principal Investigator: Juliano Antonio de Oliveira Grantee: Juliano Antonio de Oliveira Home Institution: Universidade Estadual Paulista (UNESP). Campus Experimental São João da Boa Vista. São João da Boa Vista , SP, Brazil Assoc. researchers: Edson Denis Leonel

Abstract

In this project we consider a family of one-dimensional mappings parametrised by a exponent $\gamma$ as a dynamical variable. Choosing some control parameters and a transformation in the spatial variable we recover different mappings known in the literature. We propose in this research to build orbit diagrams to analyse the dynamics of the system.We intend to study analytically and numerically the convergence to fixed points and use Lyapunov exponents to characterize the chaos. We propose extend our studies to analyse the family of two-dimensional mappings parametrized by control parameter $\gamma$. We propose introduce dissipation in the system to investigate the crisis boundary phenomena and analyse the space parameters. We restrict to the study of the Fermi-Ulam model under a action of external force. The main goals in this study is investigate analytically the average properties along of chaotic orbits to found critical expoenents to define universality classes. (AU)

Scientific publications (8)
(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)
DE OLIVEIRA, JULIANO A.; MONTERO, LEONARDO T.; DA COSTA, DIOGO R.; MENDEZ-BERMUDEZ, J. A.; MEDRANO-T, RENE O.; LEONEL, EDSON D. An investigation of the parameter space for a family of dissipative mappings. Chaos, v. 29, n. 5 MAY 2019. Web of Science Citations: 1.
DE OLIVEIRA, JULIANO A.; DE MENDONCA, HANS M. J.; DA COSTA, DIOGO R.; LEONEL, EDSON D. Effects of a parametric perturbation in the Hassell mapping. CHAOS SOLITONS & FRACTALS, v. 113, p. 238-243, AUG 2018. Web of Science Citations: 0.
DE OLIVEIRA, JULIANO A.; RAMOS, LARISSA C. N.; LEONEL, EDSON D. Dynamics towards the steady state applied for the Smith-Slatkin mapping. CHAOS SOLITONS & FRACTALS, v. 108, p. 119-122, MAR 2018. Web of Science Citations: 0.
DE MENDONCA, HANS M. J.; LEONEL, EDSON D.; DE OLIVEIRA, JULIANO A. An investigation of the convergence to the stationary state in the Hassell mapping. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 466, p. 537-543, JAN 15 2017. Web of Science Citations: 1.
MENDEZ-BERMUDEZ, J. A.; DE OLIVEIRA, JULIANO A.; LEONEL, EDSON D. Analytical description of critical dynamics for two-dimensional dissipative nonlinear maps. Physics Letters A, v. 380, n. 22-23, p. 1959-1963, MAY 20 2016. Web of Science Citations: 0.
MENDEZ-BERMUDEZ, J. A.; DE OLIVEIRA, JULIANO A.; AGUILAR-SANCHEZ, R.; LEONEL, EDSON D. Scaling properties for a family of discontinuous mappings. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 436, p. 943-951, OCT 15 2015. Web of Science Citations: 0.
DA COSTA, DIOGO RICARDO; DETTMANN, CARL P.; DE OLIVEIRA, JULIANO A.; LEONEL, EDSON D. Dynamics of classical particles in oval or elliptic billiards with a dispersing mechanism. Chaos, v. 25, n. 3 MAR 2015. Web of Science Citations: 3.
MENDEZ-BERMUDEZ, J. A.; DE OLIVEIRA, JULIANO A.; LEONEL, EDSON D. Two-dimensional nonlinear map characterized by tunable Levy flights. Physical Review E, v. 90, n. 4 OCT 27 2014. Web of Science Citations: 1.