Cdtrjyty

I was trying to replicate an image of a book, but I don't know how to increase the curvature on the curves. I've been done this so far:

documentclass[tikz, border=2pt]{standalone}

usepackage[utf8]{inputenc}

usepackage[brazilian]{babel}

usepackage{amssymb}

usepackage{tikz,tkz-euclide}

usetkzobj{all}

usepackage{xcolor}

usetikzlibrary{decorations.markings}



begin{document}

    begin{tikzpicture}[scale=3, mydot/.style={fill, circle, inner 

     sep=1.5pt}, decoration={markings, mark=at position 0.5 with 

     {arrow{latex}}}]



    draw[thick] (0,0) to[out=5,in=175, looseness=.8] (5,0);

    draw[thick] (0,0) to[out=-10,in=190, looseness=1.4] (5,0);

    draw[ultra thick] (0,0) to[out=-15,in=195, looseness=1.5] (5,0);

    draw[thick] (0,0) to[out=-25,in=205, looseness=1.6] (5,0);

    draw[thick] (0,0) to[out=-35,in=215, looseness=1.6] (5,0);

    draw[thick] (0,0) to[out=-45,in=225, looseness=1.7] (5,0);



    draw[thick] (1,-2) .. controls (2.3,-.567) and (2.5,.3) .. (2.3,1);



    draw[ultra thick,-latex,shorten >= 5pt] (2.3,-.567) to[out=45,in=45, 

    looseness=0] (2.8,.8);

    draw[ultra thick,-latex,shorten >= 5pt] (5.7,.7) to[out=190,in=80, 

    looseness=.8] (5,0);

    draw[ultra thick,-latex,shorten >= 5pt] (5,-1) to[out=120,in=1, 

    looseness=.7] (4,-.3);

    draw[ultra thick,-latex,shorten >= 5pt] (4,-2) to[out=120,in=1, 

    looseness=.7] (3.1,-1.6);



    node[mydot] at (0,0) {};

    node[mydot] at (5,0) {};



    node at (.9,-2.1) {{Large $X_p$}};

    node at (2.9,.85) {{Large $xi(p)$}};

    node at (5.85,.8) {{Large $partial M$}};

    node at (5.3,-1.1) {{Large $X_0=x$}};

    node at (4.1,-2.1) {{Large $X_t$}};

end{tikzpicture}

end{document}

The picture I want to replicate is that one bellow:

Using proper coordinates and plot command, smooth curves as shown in question can be reproduced. The format to use plot is:

draw[smooth] plot coordinates{<list of coordinates>};

A minimal working example:

documentclass[border=3mm]{standalone}

usepackage{tikz}



begin{document}

begin{tikzpicture}

fill (0,0) circle (2pt);

fill (5,0) circle (2pt);

draw[smooth,tension=0.7] plot coordinates{(0,0) (0.7,0.0) (1.8,0.2) (3.2,0.2) (4.3,0.0) (5,0)};

draw[thick,smooth,tension=0.7] plot coordinates{(0,0) (0.7,-0.1) (1.8,-0.4) (3.2,-0.4) (4.3,-0.1) (5,0)};

draw[smooth,tension=0.7] plot coordinates{(0,0) (0.7,-0.11) (1.8,-0.6) (3.2,-0.6) (4.3,-0.11) (5,0)};

draw[smooth,tension=0.7] plot coordinates{(0,0) (0.7,-0.12) (1.8,-0.7) (3.2,-0.7) (4.3,-0.12) (5,0)};

end{tikzpicture}

end{document}

Output:

Arguably, something like bend right might be better suited to produce some surface with constant mean curvature, but I am not claiming that this necessarily a closer reproduction of your screen shot. The main purpose of this answer is, however, to advertize relative positioning for the nodes and arrows.

documentclass[tikz, border=2pt]{standalone}

usepackage[utf8]{inputenc}

usepackage[brazilian]{babel}

usepackage{amssymb}

usepackage{tikz,tkz-euclide}

usetkzobj{all}

usepackage{xcolor}

usetikzlibrary{decorations.markings}



begin{document}

    begin{tikzpicture}[scale=3, mydot/.style={fill, circle, inner 

     sep=1.5pt}, decoration={markings, mark=at position 0.5 with 

     {arrow{latex}}},font=Large]



    foreach X in {-5,5,25,35,45}

    {draw[thick] (0,0) to[bend right=X] coordinate[pos=0.8] (auxX) (5,0);}

    draw[ultra thick] (0,0) to[bend right=15] coordinate[pos=0.4] (aux1) 

    coordinate[pos=0.7] (aux2) (5,0);



    draw[thick] (1,-2) node[below]{$X_p$} .. controls (2.3,-.567) and (2.5,.3) .. (2.3,1);





    draw[ultra thick,latex-] (aux1) -- ++(2,2) node[above]{

    $xi(p)$};

    draw[ultra thick,latex-] (aux2) to[bend right] ++ (1.2,-1.2) node[right]{$X_0=x$};

    draw[ultra thick,latex-] (aux35) to[bend right] ++ (1.2,-0.6)

    node[right]{$X_t$};



    node[mydot] (L) at (0,0) {};

    node[mydot] (R) at (5,0) {};

    draw[ultra thick,latex-] (R) to[bend left] ++ (1,0.5)

    node[right]{$partial M$};



end{tikzpicture}

end{document}