# Szemináriumok

## Rigorous numerics for periodic solutions to piecewise-linear delay equations

Időpont:
2018. 03. 01. 10:15
Hely:
H306
Kiss Gábor

We present a novel computational tool for establishing the existence of periodic solutions of piecewise-linear delay differential equations. The method is based on the Chebyshev expansions of solutions. As an illustration, we use a piecewise-linear approximation of the celebrated Mackey-Glass equation.

## Self-testing mutually unbiased bases in the prepare-and-measure scenario

Időpont:
2018. 02. 28. 14:00
Hely:
H306
Farkas Máté (Gdansk)

## Néhány harmadfokú felület geometriája

Időpont:
2018. 02. 27. 10:30
Hely:
H.306
Szabó Szilárd

## Invariance principle for the random Lorentz gas beyond the Boltzmann-Grad (or, Gallavotti-Spohn) limit II.

Időpont:
2018. 02. 23. 14:15
Hely:
H306
Bálint Tóth (Bristol, Rényi)

## Invariance principle for the random Lorentz gas beyond the Boltzmann-Grad (or, Gallavotti-Spohn) limit I.

Időpont:
2018. 02. 22. 16:15
Hely:
H306
Bálint Tóth (Bristol, Rényi)

## Abstract bifurcations

Időpont:
2018. 02. 22. 10:15
Hely:
H306
Kovács Sándor

Modelling of phenomena in applied sciences like physics, biology or engineering  often leads to equations depending on parameters. These parameters describe how the environment influences a system. Thus, the knowledge of the values of the parameters at which the qualitative behaviour of the system changes has great importance. In this talk we study the structure of  equations of the form $F(x,\lambda)=0,$ where $F$ is a nonlinear operator between Banach spaces and $\lambda$ represents the parameters.

## A Kneser--Poulsen-sejtés speciális kontrakciókra (The Kneser--Poulsen conjecture for special contractions)

Időpont:
2018. 02. 20. 10:30
Hely:
H.306
Naszódi Márton

## Dynamics and Delays

Időpont:
2018. 02. 16. 14:00
Hely:
H306
Krisztin Tibor (Szeged)

## The Differential Equation that Solves Every Problem or How to Lie with Universal Equations

Időpont:
2018. 02. 15. 10:15
Hely:
H306
Kalmár-Nagy Tamás

We present a new approach to the construction of first integrals for second order autonomous systems without invoking a Lagrangian or Hamiltonian reformulation. We show and exploit the analogy between integrating factors of first order equations and their Lie point symmetry and integrating factors of second order autonomous systems and their dynamical symmetry. We connect intuitive and dynamical symmetry approaches through one-to-one correspondence in the framework proposed for first order systems. Conditional equations for first integrals are written out, as well as equations determining symmetries. The equations are applied on the simple harmonic oscillator and a class of nonlinear oscillators to yield integrating factors and first integrals.

A Lie algebraic approach is also used to study universal equations. To be universal, a differential equation must have a solution with which an arbitrary function can be uniformly approximated. A universal differential equation must be form invariant under translation and scaling. We present a way to construct universal equations.

## Felsőbb elemi geometria – Tételek és problémák

Időpont:
2018. 02. 13. 10:30
Hely:
H.306