G. Contopoulos

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20242026

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nlin.CD2026

Limits of the Formal Integrals of Motion

George Contopoulos, Athanasios C. Tzemos, Foivos Zanias

We consider a formal (approximate) integral of motion in Hamiltonians of the form $H = \frac{1}{2} (X^{2} + Y^{2} + I ¨ _{1}^{2} x^{2} + I ¨ _{2}^{2} y^{2}) + I^µ (I^\cdot x y^{2} + I^\pm x^{3} + I^^{2} x^{2} y + I^^{3} y^{3})$ generalizing previous c…

nlin.CD2025

Orbits in the integrable HÃ©non-Heiles systems

Athanasios C. Tzemos, George Contopoulos, Foivos Zanias

We study in detail the form of the orbits in integrable generalized HÃ©non-Heiles systems with Hamiltonians of the form $H = \frac{1}{2}(\dot{x}^2 + Ax^2 + \dot{y}^2 + By^2) + Îµ(x…

nlin.CD2025

G. Contopoulos, A. C. Tzemos, F. Zanias

We study the approximate (formal) integrals of motion in the Hamiltonian $H = \frac{1}{2} (x ˙^{2} + y ˙^{2} + x^{2} + y^{2}) + I^µ (x y^{2} + I^\pm x^{3})$ which i…

nlin.CD2024

Classical and Bohmian trajectories in integrable and non integrable systems

George Contopoulos, Athanasios C. Tzemos

In the present paper we study the classical and the quantum HÃ©non-Heiles systems. In particular we make a comparison between the classical and the quantum trajectories of the inte…

Limits of the Formal Integrals of Motion

Orbits in the integrable HÃ©non-Heiles systems

Integrals and chaos in generalized HÃ©non-Heiles Hamiltonians

Classical and Bohmian trajectories in integrable and non integrable systems