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### MS13 - Discontinuous dynamical systems: theory and numerical methods

Organized by: **Luciano Lopez and Cinzia Elia**

*Models are often described by discontinuous ODEs or discontinuous dynamical systems. The discontinuity can occur in the solution (impact systems) or in the vector field of the differential system (Filippov systems). Filippv differential systems may show solutions which cross or slide one or more discontinuous surfaces. Several questions, both of theoretical and numerical type, arise in the mathematical treatment of such problems as the loss of uniqueness of the solution or the loss of accuracy of standard numerical schemes for ODEs. In this minisymposium we would discuss these aspects of discontinuous ODEs. *

#### Invited Contributions

- A novel method to compute Lyapunov exponents of switched linear systems (I)

Marino Zennaro

*Dipartimento di Matematica e Geoscienze, Università di Trieste (Italy)* - A novel method to compute Lyapunov exponents of switched linear systems (II)

Marino Zennaro

*Dipartimento di Matematica e Geoscienze, Università di Trieste (Italy)* - Optimal adaptive approximation of a class of non-autonomous IVPs with unknown singularities

Paweł Przybyłowicz

*AGH University of Science and Technology, Faculty of Applied Mathematics, Krakow (Poland)* - A Filippov sliding vector field on a codimension 2 surface. Theoretical justifications

Cinzia Elia

*University of Bari (Italy)* - Runge-Kutta methods for the numerical solution of discontinuous systems of Filipov's type

Juan Ignacio Montijano

*Universidad de Zaragoza (Spain)* - Numerical solution of fractional differential equations with discontinuous right-hand side

Roberto Garrappa

*University of Bari (Italy)* - One-sided numerical methods to locate event points in discontinuous ODEs

Luciano Lopez

*Department of Mathematics, University of Bari (Italy)*