Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion: Homoclinic orbits, and self-excited and hidden …

GA Leonov, NV Kuznetsov, TN Mokaev - The European Physical Journal …, 2015 - Springer
In this paper, we discuss self-excited and hidden attractors for systems of differential
equations. We considered the example of a Lorenz-like system derived from the well-known …

Dynamics of Loschmidt echoes and fidelity decay

T Gorin, T Prosen, TH Seligman, M Žnidarič - Physics Reports, 2006 - Elsevier
Fidelity serves as a benchmark for the reliability in quantum information processes, and has
recently attracted much interest as a measure of the susceptibility of dynamics to …

Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system

NV Kuznetsov, GA Leonov, TN Mokaev, A Prasad… - Nonlinear …, 2018 - Springer
The Rabinovich system, describing the process of interaction between waves in plasma, is
considered. It is shown that the Rabinovich system can exhibit a hidden attractor in the case …

[HTML][HTML] On differences and similarities in the analysis of Lorenz, Chen, and Lu systems

GA Leonov, NV Kuznetsov - Applied Mathematics and Computation, 2015 - Elsevier
Currently it is being actively discussed the question of the equivalence of various Lorenz-like
systems and the possibility of universal consideration of their behavior (Algaba et al., 2013a …

[BOOK][B] Nonlinear dynamics and quantum chaos

S Wimberger - 2014 - Springer
Sandro Wimberger An Introduction Second Edition Page 1 Nonlinear Dynamics and
Quantum Chaos Sandro Wimberger An Introduction Second Edition Graduate Texts in …

Geometrical properties of local dynamics in Hamiltonian systems: The Generalized Alignment Index (GALI) method

C Skokos, TC Bountis, C Antonopoulos - Physica D: Nonlinear Phenomena, 2007 - Elsevier
We investigate the detailed dynamics of multi-dimensional Hamiltonian systems by studying
the evolution of volume elements formed by unit deviation vectors about their orbits. The …

[HTML][HTML] The Lyapunov dimension and its estimation via the Leonov method

NV Kuznetsov - Physics Letters A, 2016 - Elsevier
Along with widely used numerical methods for estimating and computing the Lyapunov
dimension there is an effective analytical approach, proposed by GA Leonov in 1991. The …

Lyapunov dimension formula for the global attractor of the Lorenz system

GA Leonov, NV Kuznetsov, NA Korzhemanova… - … in Nonlinear Science …, 2016 - Elsevier
The exact Lyapunov dimension formula for the Lorenz system for a positive measure set of
parameters, including classical values, was analytically obtained first by GA Leonov in 2002 …

Data-driven approximations of dynamical systems operators for control

E Kaiser, JN Kutz, SL Brunton - The Koopman operator in systems and …, 2020 - Springer
Abstract The Koopman and Perron Frobenius transport operators are fundamentally
changing how we approach dynamical systems, providing linear representations for even …

Quantum many-body scars from unstable periodic orbits

B Evrard, A Pizzi, SI Mistakidis, CB Dag - Physical Review B, 2024 - APS
Unstable periodic orbits (UPOs) play a key role in the theory of chaos, constituting the
“skeleton” of classical chaotic systems and “scarring” the eigenstates of the corresponding …