11 problems

Consider a continuous Rayleigh system $(L,\mathcal{R})$ on $TQ$, where $L$ is natural, meaning that … Here $g$ is a Riemannian metric on $Q$ and $V$ is a function on $Q$. Let…

Consider a classical deterministic system with loss of information, interpreted as dissipation, and impose suitable constraints and specific energy conditions. 't Hooft's conjectur…

The paper discusses coupled Bose–Einstein systems with dissipative effects, described by effective Hamiltonians that need not be Hermitian. Simple effective-Hamiltonian conjecture.…

Consider the semilinear dissipative Timoshenko system with equal wave speeds, let $p$ be the power of its semilinear term, and write $p_{\mathrm{Fuj}}(1)=3$. The paper establishes…

Consider semilinear Timoshenko systems with the various dissipations studied in the cited works, and let $p$ denote the power of the semilinear term. Sharpness conjecture. The rest…

Generation conjecture. Conversely, any maximally monotone subspace $Mathcal M$ can be generated as

A mechanical system consists of a rotator and a pendulum coupled by a small, time-periodic Hamiltonian perturbation; Arnold diffusion refers to diffusing orbits along which the rot…

Let $f_{\varepsilon}$ be the conformally symplectic dissipative standard map with complex parameter $\varepsilon$, and let the invariant tori be the quasi-periodic invariant circle…

Consider a Hamiltonian chain of rotators with a dissipative evolution, and let a quasi-stationary state be a state whose actions and angles have the slowly varying, oscillatory sca…

Dissipative frequency-parameterization conjecture. There exists a diffeomorphism $\Xi(\vet{\omega},\vet{\varphi})$ satisfying the same properties (I)--(III) as the diffeomorphism…

Let $u: \mathbb{R} \times \mathbb{R}_+ \to \mathbb{R}$ solve the parabolic equation with initial data $u_0$ satisfying … where $(b_n)_{n\in\mathbb{N}}$ is strictly increasing,…