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Exponents and scaling laws, phase transitions and transport properties of time dependent systems

Abstract

The main goal of this project is to understand and describe somenonlinear phenomena particularly concentrated in phase transitions fromintegrability to non integrability. The phase space is of mixed typeand contains KAM islands, invariant spanning curves and chaotic seas.The size of the chaotic sea and the average properties for such regionin the phase space is strongly dependent on the position of the firstinvariant spanning curve. We shall concentrate in the description ofsuch curve by using a connection with the standard mapping. Averageproperties and transport of particles along the chaotic sea will beconsidered too. Possible connections equilibrium states of billiardswith thermodynamics are desired to be obtained using the so called timedependent billiard systems. (AU)

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Scientific publications (42)
(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)
HANSEN, MATHEUS; DA COSTA, DIOGO R.; OLIVEIRA, DIEGO F. M.; LEONEL, EDSON D.. Statistical properties for a dissipative model of relativistic particles in a wave packet: A parameter space investigation. Applied Mathematics and Computation, v. 238, p. 387-392, . (13/01449-1, 12/23688-5, 12/18962-0, 13/22764-2)
LEONEL, EDSON D.; LIVORATI, ANDE L. P.; CESPEDES, ANDRE M.. A theoretical characterization of scaling properties in a bouncing ball system. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 404, p. 279-284, . (12/23688-5)
DA COSTA, DIOGO RICARDO; OLIVEIRA, DIEGO F. M.; LEONEL, EDSON D.. Dynamical and statistical properties of a rotating oval billiard. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 19, n. 6, p. 1926-1934, . (12/18962-0, 13/01449-1, 12/23688-5)
TEIXEIRA, RIVANIA M. N.; RANDO, DANILO S.; GERALDO, FELIPE C.; COSTA FILHO, R. N.; DE OLIVEIRA, JULIANO A.; LEONEL, EDSON D.. Convergence towards asymptotic state in 1-D mappings: A scaling investigation. Physics Letters A, v. 379, n. 18-19, p. 1246-1250, . (12/23688-5)
GRACIANO, FLAVIO HELENO; DA COSTA, DIOGO RICARDO; LEONEL, EDSON D.; DE OLIVEIRA, JULIANO A.. Multiple Reflections for Classical Particles Moving under the Influence of a Time-Dependent Potential Well. Entropy, v. 24, n. 10, p. 15-pg., . (17/14414-2, 21/09519-5, 19/14038-6, 20/02415-7, 12/23688-5, 18/14685-9)
PALMERO, MATHEUS S.; LIVORATI, ANDRE L. P.; CALDAS, IBERE L.; LEONEL, EDSON D.. Ensemble separation and stickiness influence in a driven stadium-like billiard: A Lyapunov exponents analysis. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 65, p. 248-259, . (17/14414-2, 14/25316-3, 12/23688-5, 12/00556-6, 15/26699-6, 11/19296-1)
DE OLIVEIRA, JULIANO A.; DE MENDONCA, HANS M. J.; DA SILVA, ANDERSON A. A.; LEONEL, EDSON D.. Critical Slowing Down at a Fold and a Period Doubling Bifurcations for a Gauss Map. Brazilian Journal of Physics, v. 49, n. 6, p. 923-927, . (18/14685-9, 15/22062-3, 14/18672-8, 17/14414-2, 12/23688-5)
LEONEL, EDSON D.. Defining universality classes for three different local bifurcations. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 39, p. 520-528, . (12/23688-5)
LIVORATI, ANDRE L. P.; CALDAS, IBERE L.; DETTMANN, CARL P.; LEONEL, EDSON D.. Crises in a dissipative bouncing ball model. Physics Letters A, v. 379, n. 43-44, p. 2830-2838, . (12/23688-5, 14/25316-3, 11/19296-1)
MENDEZ-BERMUDEZ, J. A.; MARTINEZ-MENDOZA, A. J.; LIVORATI, ANDRE L. P.; LEONEL, EDSON D.. Leaking of trajectories from the phase space of discontinuous dynamics. Journal of Physics A-Mathematical and Theoretical, v. 48, n. 40, . (14/25997-0, 13/14655-9, 12/23688-5, 14/25316-3)
DE OLIVEIRA, JULIANO A.; DE MENDONCA, HANS M. J.; FAVARIM, VITOR A.; DE CARVALHO, R. EGYDIO; LEONEL, EDSON D.. Boundary crises and supertrack orbits in the Gauss map. European Physical Journal-Special Topics, v. 231, n. 3, p. 4-pg., . (21/09519-5, 12/23688-5, 19/07329-4, 18/14685-9, 15/22062-3, 19/14038-6)
KROETZ, TIAGO; LIVORATI, ANDRE L. P.; LEONEL, EDSON D.; CALDAS, IBERE L.. Global ballistic acceleration in a bouncing-ball model. Physical Review E, v. 92, n. 1, p. 11-pg., . (11/19296-1, 12/23688-5, 14/25316-3)
OLIVEIRA, DIEGO F. M.; LEONE, EDSON D.. Statistical and dynamical properties of a dissipative kicked rotator. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 413, p. 498-514, . (12/23688-5)
LIVORATI, ANDRE L. P.; PALMERO, MATHEUS S.; DETTMANN, CARL P.; CALDAS, IBERE L.; LEONEL, EDSON D.. Separation of particles leading either to decay or unlimited growth of energy in a driven stadium-like billiard. Journal of Physics A-Mathematical and Theoretical, v. 47, n. 36, . (12/23688-5, 12/00556-6, 11/19296-1)
AGUILAR-SANCHEZ, R.; LEONEL, EDSON D.; MENDEZ-BERMUDEZ, J. A.. Dynamical properties of a dissipative discontinuous map: A scaling investigation. Physics Letters A, v. 377, n. 44, p. 3216-3222, . (12/23688-5)
DA COSTA, DIOGO RICARDO; CALDAS, IBERE L.; LEONEL, EDSON D.. Phase space properties and chaotic transport for a particle moving in a time dependent step potential well. Applied Mathematics and Computation, v. 236, p. 215-228, . (12/23688-5, 12/18962-0)
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, p. 5-pg., . (12/23688-5, 13/14655-9, 14/18672-8)
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, . (15/22062-3, 14/18672-8, 17/14414-2, 12/23688-5)
DE FARIA, NILSON B.; TAVARES, DANIEL S.; DE PAULA, WENDERSON C. S.; LEONEL, EDSON D.; LADEIRA, DENIS G.. Transport of chaotic trajectories from regions distant from or near to structures of regular motion of the Fermi-Ulam model. PHYSICAL REVIEW E, v. 94, n. 4, p. 9-pg., . (12/23688-5)
LEONEL, EDSON D.; CAMILLO GALIA, MARCUS VINICIUS; BARREIRO, LUIZ ANTONIO; OLIVEIRA, DIEGO F. M.. Thermodynamics of a time-dependent and dissipative oval billiard: A heat transfer and billiard approach. PHYSICAL REVIEW E, v. 94, n. 6, p. 10-pg., . (12/23688-5)
LEONEL, EDSON D.; KUWANA, CELIA M.. An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action. Journal of Statistical Physics, v. 170, n. 1, p. 69-78, . (17/14414-2, 12/23688-5)
HANSEN, MATHEUS; DA COSTA, DIOGO RICARDO; CALDAS, IBERE L.; LEONEL, EDSON D.. Statistical properties for an open oval billiard: An investigation of the escaping basins. CHAOS SOLITONS & FRACTALS, v. 106, p. 355-362, . (17/14414-2, 12/23688-5, 13/22764-2, 14/00334-9, 11/19296-1)
EGYDIO DE CARVALHO, R.; LEONEL, EDSON D.. Squared sine logistic map. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 463, p. 37-44, . (12/23688-5, 14/00334-9)
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, . (12/23688-5, 14/18672-8, 12/18962-0, 13/22764-2)
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, . (14/18672-8, 12/23688-5, 15/22062-3)
CAMILLO GALIA, MARCUS VINICIUS; OLIVEIRA, DIEGO F. M.; LEONEL, EDSON D.. Evolution to the equilibrium in a dissipative and time dependent billiard. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 465, p. 66-74, . (12/23688-5)
LEONEL, EDSON D.; CAMILLO GALIA, MARCUS VINICIUS; BARREIRO, LUIZ ANTONIO; OLIVEIRA, DIEGO F. M.. Thermodynamics of a time-dependent and dissipative oval billiard: A heat transfer and billiard approach. Physical Review E, v. 94, n. 6, . (12/23688-5)
KROETZ, TIAGO; LIVORATI, ANDRE L. P.; LEONEL, EDSON D.; CALDAS, IBERE L.. Global ballistic acceleration in a bouncing-ball model. Physical Review E, v. 92, n. 1, . (12/23688-5, 14/25316-3, 11/19296-1)
OLIVEIRA, DIEGO F. M.; SILVA, MARIO ROBERTO; LEONEL, EDSON D.. A symmetry break in energy distribution and a biased random walk behavior causing unlimited diffusion in a two dimensional mapping. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 436, p. 909-915, . (13/01449-1, 12/23688-5)
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, . (12/23688-5, 14/25997-0, 13/14655-9, 14/18672-8)
LEONEL, EDSON D.; PENALVA, JULIA; TEIXEIRA, RIVANIA M. N.; COSTA FILHO, RAIMUNDO N.; SILVA, MARIO R.; DE OLIVEIRA, JULIANO A.. A dynamical phase transition for a family of Hamiltonian mappings: A phenomenological investigation to obtain the critical exponents. Physics Letters A, v. 379, n. 32-33, p. 1808-1815, . (12/23688-5)
DIAZ, I, GABRIEL; LIVORATI, ANDRE L. P.; LEONEL, EDSON D.. Statistical investigation and thermal properties for a 1-D impact system with dissipation. Physics Letters A, v. 380, n. 21, p. 1830-1838, . (12/23688-5, 14/25316-3)
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, . (12/23688-5, 14/25997-0, 13/14655-9, 14/18672-8)
LIVORATI, ANDRE L. P.; PALMERO, MATHEUS S.; DIAZ-, I, GABRIEL; DETTMANN, CARL P.; CALDAS, IBERE L.; LEONEL, EDSON D.. Investigation of stickiness influence in the anomalous transport and diffusion for a non-dissipative Fermi-Ulam model. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 55, p. 225-236, . (14/25316-3, 12/23688-5, 15/26699-6, 14/27260-5)
DA COSTA, DIOGO RICARDO; DETTMANN, CARL P.; LEONEL, EDSON D.. Circular, elliptic and oval billiards in a gravitational field. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 22, n. 1-3, p. 731-746, . (12/18962-0, 13/22764-2, 12/23688-5)
LEONEL, EDSON D.; LIVORATI, ANDRE L. P.. Thermodynamics of a bouncer model: A simplified one-dimensional gas. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 20, n. 1, p. 159-173, . (12/23688-5)
HANSEN, MATHEUS; EGYDIO DE CARVALHO, R.; LEONEL, EDSON D.. Influence of stability islands in the recurrence of particles in a static oval billiard with holes. Physics Letters A, v. 380, n. 43, p. 3634-3639, . (12/23688-5, 14/00334-9)
DE FARIA, NILSON B.; TAVARES, DANIEL S.; DE PAULA, WENDERSON C. S.; LEONEL, EDSON D.; LADEIRA, DENIS G.. Transport of chaotic trajectories from regions distant from or near to structures of regular motion of the Fermi-Ulam model. Physical Review E, v. 94, n. 4, . (12/23688-5)
LIVORATI, A. L. P.; DE OLIVEIRA, J. A.; LADEIRA, D. G.; LEONEL, E. D.. Time-dependent properties in two-dimensional and Hamiltonian mappings. European Physical Journal-Special Topics, v. 223, n. 13, p. 2953-2958, . (12/23688-5)
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, . (13/14655-9, 14/18672-8, 12/23688-5)
LIVORATI, ANDRE L. P.; DETTMANN, CARL P.; CALDAS, IBERE L.; LEONEL, EDSON D.. On the statistical and transport properties of a non-dissipative Fermi-Ulam model. Chaos, v. 25, n. 10, . (12/23688-5, 14/25316-3, 11/19296-1)
LIVORATI, ANDRE L. P.; GEORGIOU, ORESTIS; DETTMANN, CARL P.; LEONEL, EDSON D.. Escape through a time-dependent hole in the doubling map. Physical Review E, v. 89, n. 5, . (12/23688-5)

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