| Grant number: | 12/18962-0 |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |
| Effective date (Start): | February 01, 2013 |
| Effective date (End): | July 31, 2013 |
| Field of knowledge: | Physical Sciences and Mathematics - Physics - General Physics |
| Principal Investigator: | Edson Denis Leonel |
| Grantee: | Diogo Ricardo da Costa |
| Supervisor: | Carl Dettmann |
| Host Institution: | Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil |
| Research place: | University of Bristol, England |
Abstract We will investigate some escape and dynamical properties for an ensemble of non-interacting particles moving in closed domains. When a holeor a escape region is introduced in the phase space, the histogram for the number of particles that escaped, which is scaling invariant, grows rapidly reaching a maximum and tends to zero for long enough time. The systems proposed here have a mixed phase space, containing KAM islands, chaotic seas and invariant spanning curves (ISC). Considering the position of the hole as proprotional to the first ISC, we can find some critical exponents, confirming a scaling invariance. In this project we consider anoval/elliptic billiard that contains a small circle in the horizontal axis, which is a generalization of the annular and Sinai billiards. Another problem of our interest is the characterization of the families of marginally unstable periodic orbits (MUPOs) in mushroom billiard, considering circular and elliptical hats. We therefore will try to obtain the dimension of the set without MUPOs as a function of the base length $r$, and the presence of stickiness in mushroooms without these MUPOs. As we know the curve $y=x^4$ has curvature that approaches zero at the point $x=0$, and so violates the strict focussing property. This meansthere may be trajectories that are sticky to the extent that they have an infinite number of regular collisions in a finite time. We propose toinvestigate its properties and effect on the dynamics of the whole billiard. The last problem that we propose is to investigate the resulting stickiness and its effect on the dynamics of the whole billiard in a cusp composed for a dispersing and focusing edge (it is made considering two non-concentric circles). In this case, there may be an unbounded number of collisions in a finite time as the trajectory enters the region between the two circles. (AU) | |
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