The talk is scheduled in virtual setting, using Zoom platform. The talk will also be live-streamed via YouTube. During the meeting, the questions can be posed via chat or audio for participants in the meeting. Everybody interested is invited to participate in the Zoom meeting, with the limit of 100 participants, or to follow the live-broadcast.
Link to Zoom meeting will be put here few days before the talk:
https://us02web.zoom.us/j/89253380963
Meeting ID: 892 5338 0963
Link to YouTube live broadcast will be put here 10 minutes before the talk.
http://www.youtube.com/watch?v=IMduzy1GyIA
The talk will be in English.
ABSTRACT:
We start showing that for planar periodic non-autonomous discrete dynamical systems,
even when a common fixed point for each of the autonomous associated dynamical
systems is repeller, this fixed point can became a local attractor for the
whole system, giving rise to a Parrondo’s dynamical type paradox. This result can
be easily extended to even dimension.
Afterwards we study a similar situation, involving two planar homeomorphisms.
This planar construction can also be extended to any dimension greater than 2 and
shows the appearance of the dynamical Parrondo’s paradox in odd dimensions.
Finally this paradox is proved to appear also in two other situations:
• Some iterated function system generated by two maps f and g, where each of
them appears with a certain probability; and
• Some planar alternating ordinary differential equations, which can be used to
model systems with seasonality.
The talk is based on the papers:
A. Cima, A. Gasull, V. Mañosa. Parrondo's dynamic paradox for the
stability of non-hyperbolic xed points. Discrete Contin. Dyn. Syst.
38 (2018) 889-904.
A. Cima, A. Gasull, V. Mañosa. A dynamic Parrondo's paradox for
continuous seasonal systems. Nonlinear Dynam. 102 (2020)
1033-1043.
A. Gasull, L. Hernandez-Corbato, F. R. Ruiz del Portal. Parrondo's
paradox for homeomorphisms. To appear in Proc. Roy. Soc.
Edinburgh Sect. A.
